Trigonometry and triangles
•Download as PPTX, PDF•
0 likes•309 views
Trigonometry deals with relationships between the sides and angles of triangles. It uses trigonometric functions like sine, cosine, and tangent. Sine relates the opposite side to the hypotenuse, cosine relates the adjacent side to the hypotenuse, and tangent relates the opposite side to the adjacent side. Trigonometry can be used to find unknown side lengths or angles in triangles, including solving "story problems" where trigonometric applications are needed to determine real-world measurements. The document provides examples of using trigonometric functions like sine, cosine, and tangent to solve for unknown values in right and non-right triangles, as well as how to set up and solve word problems involving trigonometric applications.
Report
Share
Report
Share
Recommended
Trigonometryandtriangles 110929154951-phpapp02
This document discusses trigonometry and its applications to triangles. It introduces the key trigonometric functions of sine, cosine, and tangent using the ratios of sides in right triangles. These ratios are summarized by the mnemonic SOH CAH TOA. Examples are provided to demonstrate using trigonometric functions to find unknown side lengths, angles, and areas of triangles. Non-right triangles are also discussed along with example story problems involving trigonometry.
Right triangles day2
1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles.
2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles.
3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
Formular
The document provides formulas and definitions for various topics in geometry, algebra, trigonometry, and other areas of mathematics. Some of the key information presented includes formulas for calculating the volume and surface area of geometric solids like cubes, cylinders, and cones. In algebra, formulas are given for exponent rules, factoring, and solving equations. Trigonometry formulas define the trigonometric functions and include basic identities. Graphs of common functions like linear, quadratic, and trigonometric functions are also depicted.
Powerpoint(pythagorean theorem)
The document discusses the Pythagorean theorem and its applications to right triangles. It defines the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. It provides examples of using the Pythagorean theorem to calculate missing sides of right triangles when given two sides. Exercises at the end ask the reader to apply the Pythagorean theorem to find missing sides of right triangles.
Right triangle problems
This document discusses solving right triangle problems using trigonometric functions like sine, cosine, and tangent. It provides examples of right triangles where certain sides or angles are given and asks the reader to solve for unknown values. Applications discussed include finding the length of a pole or distance across a river using right triangles defined by angles of elevation or depression. Bearings and courses of ships are also defined and used in an example of finding distance and bearings between two moving ships after a period of time.
Trigonometry
This document discusses trigonometric ratios and functions. It defines the sine, cosine, and tangent ratios for right triangles. It also introduces the reciprocal functions of cosecant, secant, and cotangent. Special angle values for trig functions are provided in a table. The document explains how to write trig functions in terms of x, y, and r using the Cartesian plane and use a CAST diagram to determine the quadrants where trig ratios are positive and negative. Finally, it discusses extending knowledge of special angles using trig ratio definitions in the Cartesian plane.
Grade 12 Unit1-L1-Kinematic Equations
This document provides an overview and review of kinematics concepts including:
1) Defining directions as positive or negative is important to avoid errors in kinematics problems.
2) Five fundamental kinematics equations are presented that assume constant or zero acceleration and deal with displacement, velocity, acceleration, and time.
3) An example problem is provided and instructions are given for homework practice problems to reinforce kinematics concepts.
Exam 6232 A
1. The document contains 11 multi-part math problems involving trigonometric functions such as sine, cosine, tangent, and cotangent. The problems involve verifying trigonometric identities, finding unknown side lengths and angles of right triangles, solving for trigonometric functions given angle measures, and solving application word problems involving angles of elevation or depression.
2. The problems require using trigonometric functions, identities, properties of right triangles, and applications of trigonometry to solve for unknown values. Multiple steps may be needed to arrive at the solutions, which generally involve setting up and solving equations.
3. The level of detail of the problems ranges from simply finding specific function values to solving multi-step
Recommended
Trigonometryandtriangles 110929154951-phpapp02
This document discusses trigonometry and its applications to triangles. It introduces the key trigonometric functions of sine, cosine, and tangent using the ratios of sides in right triangles. These ratios are summarized by the mnemonic SOH CAH TOA. Examples are provided to demonstrate using trigonometric functions to find unknown side lengths, angles, and areas of triangles. Non-right triangles are also discussed along with example story problems involving trigonometry.
Right triangles day2
1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles.
2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles.
3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
Formular
The document provides formulas and definitions for various topics in geometry, algebra, trigonometry, and other areas of mathematics. Some of the key information presented includes formulas for calculating the volume and surface area of geometric solids like cubes, cylinders, and cones. In algebra, formulas are given for exponent rules, factoring, and solving equations. Trigonometry formulas define the trigonometric functions and include basic identities. Graphs of common functions like linear, quadratic, and trigonometric functions are also depicted.
Powerpoint(pythagorean theorem)
The document discusses the Pythagorean theorem and its applications to right triangles. It defines the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. It provides examples of using the Pythagorean theorem to calculate missing sides of right triangles when given two sides. Exercises at the end ask the reader to apply the Pythagorean theorem to find missing sides of right triangles.
Right triangle problems
This document discusses solving right triangle problems using trigonometric functions like sine, cosine, and tangent. It provides examples of right triangles where certain sides or angles are given and asks the reader to solve for unknown values. Applications discussed include finding the length of a pole or distance across a river using right triangles defined by angles of elevation or depression. Bearings and courses of ships are also defined and used in an example of finding distance and bearings between two moving ships after a period of time.
Trigonometry
This document discusses trigonometric ratios and functions. It defines the sine, cosine, and tangent ratios for right triangles. It also introduces the reciprocal functions of cosecant, secant, and cotangent. Special angle values for trig functions are provided in a table. The document explains how to write trig functions in terms of x, y, and r using the Cartesian plane and use a CAST diagram to determine the quadrants where trig ratios are positive and negative. Finally, it discusses extending knowledge of special angles using trig ratio definitions in the Cartesian plane.
Grade 12 Unit1-L1-Kinematic Equations
This document provides an overview and review of kinematics concepts including:
1) Defining directions as positive or negative is important to avoid errors in kinematics problems.
2) Five fundamental kinematics equations are presented that assume constant or zero acceleration and deal with displacement, velocity, acceleration, and time.
3) An example problem is provided and instructions are given for homework practice problems to reinforce kinematics concepts.
Exam 6232 A
1. The document contains 11 multi-part math problems involving trigonometric functions such as sine, cosine, tangent, and cotangent. The problems involve verifying trigonometric identities, finding unknown side lengths and angles of right triangles, solving for trigonometric functions given angle measures, and solving application word problems involving angles of elevation or depression.
2. The problems require using trigonometric functions, identities, properties of right triangles, and applications of trigonometry to solve for unknown values. Multiple steps may be needed to arrive at the solutions, which generally involve setting up and solving equations.
3. The level of detail of the problems ranges from simply finding specific function values to solving multi-step
Trigonometry - Strand 3
The document provides information about trigonometry topics for a foundation level class including: solving problems using right triangles, the Pythagorean theorem, defining trig functions like sine, cosine, and tangent for all angle values, graphing periodic trig functions like sine and cosine waves, and noting that the tangent graph has periods of 180 degrees and vertical asymptotes every 90 degrees.
Trig right triangle trig
This document provides examples and explanations of right triangle trigonometry concepts, including:
1) Finding trigonometric ratios (sine, cosine, tangent) for given angles in right triangles.
2) Using trigonometric functions to find missing side lengths, including for special 30-60-90 and 45-45-90 right triangles.
3) Applying trigonometry to real-world problems involving angles of elevation/depression and finding distances.
Reciprocal trig functions (cosecant, secant, cotangent) and the Pythagorean theorem are also discussed. Practice problems are provided to test understanding.
Solution of triangle
The document provides examples of solving right triangles using trigonometric functions. It first introduces right triangles and trigonometry. It then works through multiple examples, such as calculating the altitude of a plane given the horizontal distance traveled and angle of ascent. The examples demonstrate using trigonometric functions like tangent, cosine, and sine to solve for unknown sides and angles of right triangles based on given information.
Ks5 trigonometry
This document contains trigonometric identities and questions about trigonometric functions. It asks about the values of sin90, cos0, and which trig functions repeat every 2π radians. It also contains true/false questions about trig function equations and identities involving sin, cos, and tan. Finally, it asks which of several trig identities are correct.
11.2 Pythagorean Theorem
The document provides information about the Pythagorean theorem and right triangles:
1) It defines the key terms related to right triangles - the legs are the two sides adjacent to the right angle, and the hypotenuse is the side opposite the right angle.
2) It presents the Pythagorean theorem formula - a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
3) It provides examples of using the theorem to determine the length of missing sides of right triangles.
5 2slope
The document discusses slope and how to calculate it. It provides examples of slope in building roofs, hiking hills, and graphing linear equations. It emphasizes that slope is rise over run, where rise is the vertical change and run is the horizontal change between two points on a line. Instructions are given to find the slope of a line by taking the vertical and horizontal differences between two points and writing the ratio as a fraction.
Ms1 trig ratio
The document discusses trigonometry and using a scientific calculator to solve trigonometric problems involving right triangles. It defines the sides of a right triangle as the hypotenuse, opposite, and adjacent sides. It explains how to use the sine, cosine, and tangent functions on a calculator to find missing angles and sides of a triangle when given other information. Examples are provided for finding unknown angles from side lengths and unknown sides when given an angle measure. The document also addresses situations where the unknown value is on the bottom of a trigonometric ratio fraction.
Space diagonal lesson
(1) A space diagonal is a line that connects opposite vertices through the center of a rectangular prism.
(2) The Pythagorean theorem can be used to calculate the length of a space diagonal by treating it as the hypotenuse of a right triangle formed by the dimensions of the prism.
(3) For example, in a prism measuring 28cm by 12cm by 16cm, the space diagonal AG is calculated to be 34.4cm using the Pythagorean theorem and considering triangles ABC and ACG.
Trig overview
This document provides an overview of the six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. It defines these functions using ratios on the unit circle, and provides the value of each function at 30°, 45°, 60°, 90°, 135°, 150°, 225°, 300°, and 315° angles. It also explains that the trig functions repeat in the four quadrants of the unit circle, with the signs of x and y values changing depending on the quadrant.
OPERASI BILANGAN BULAT
Bilangan Bulat terdiri dari semua bilangan positif, nol, bilangan bulat negatif tanpa pecahan dan komponen desimal
Trig relationships
This document discusses trigonometric relationships between related angles. It contains the following rules:
1) sin(a) = sin(180 - a) and cos(a) = cos(180 - a), meaning trig functions of complementary angles are equal.
2) sin(a) = sin(-a) and cos(a) = cos(-a), meaning trig functions of coterminal angles are equal.
3) sin(a) = cos(90 - a) and cos(a) = sin(90 - a), relating trig functions that are 90 degrees out of phase.
Trigonometric Identities.
The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.
Chapter 3
This document summarizes key concepts about two-dimensional motion and vectors:
1) It introduces scalars, which have magnitude but no direction, and vectors, which have both magnitude and direction.
2) It describes methods for adding vectors graphically by drawing them as arrows and finding the resultant, or using trigonometry.
3) It explains projectile motion as objects moving under gravity with both horizontal and vertical components of motion that can be analyzed separately using kinematic equations.
Pythagorean Theorem Tutorial
This document provides a tutorial on using the Pythagorean theorem to solve for missing sides of right triangles. It explains the theorem and its formula, how to identify the sides of a right triangle, and how to solve for both missing hypotenuses and legs. Examples are worked through step-by-step and opportunities for practice are provided throughout the tutorial. The goal is for students to demonstrate mastery in solving for missing sides of right triangles.
6.1 Triangle Angle Relationships
Find the measures of missing angles of triangles
Find the measures of missing remote interior and exterior angles
Five most comprehensive examples of triangle laws
Triangle laws made simpler with these 5 comprehensive examples of Triangle law problems by Transtutors
Pythagorean Theorem Lesson
The document discusses the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It defines the key terms hypotenuse, legs, and explains the a^2 + b^2 = c^2 formula. Examples are given to demonstrate applying the theorem to find the unknown side of a right triangle given the other two sides. Practice problems are provided to reinforce the concept.
trigonometric ratio of 45
This document discusses trigonometric ratios of 450 angles. It begins by introducing trigonometry and defining types of triangles. It then specifies a right triangle with angles of 450. Through using Pythagorean theorem and the fact that two sides are equal, it derives the trigonometric ratios of sin 450, cos 450, and tan 450. Examples are also provided to demonstrate using the derived ratios. The key ratios are:
- Sin 450 = 1/√2
- Cos 450 = 1/√2
- Tan 450 = 1
Using sohcahtoa
(3) slide presentation that walks through the utilization of the SOH CAH TOA formulas, including how to plug functions into the calculator.
SCORE: strengthening student engagement
The document discusses different factors that can strengthen student engagement:
1) It identifies five main goals (Success, Curiosity, Originality, Relationships, Energy) that drive student engagement as they satisfy basic human needs.
2) For Success, it recommends clearly defining criteria for success and providing feedback to help students see skills as achievable.
3) To arouse Curiosity, it suggests providing incomplete information to compel understanding.
4) For Originality, it advises connecting creative projects to students' interests and expanding what counts as audiences.
5) Fostering Relationships involves complementary assignments and structured group work.
Pc 4.1 notes
This document discusses radians and degree measures of angles. Some key points:
- A radian is the measure of a central angle that intercepts an arc equal in length to the radius of the circle. There are 2π radians in a full circle.
- Coterminal angles have the same initial and terminal sides and can be obtained by adding or subtracting full revolutions (2π) to an angle measure.
- The document provides examples of converting between degrees and radians and finding coterminal angles.
Neural tube defects and Craniosynostosis
This document discusses various congenital anomalies that affect the central nervous system, including neural tube defects (NTDs) such as spina bifida occulta, meningocele, meningomyelocele, encephalocele, and anencephaly. It describes the embryology of neural tube formation and risk factors for NTDs such as folic acid deficiency. The document also discusses craniosynostosis, which is the premature fusion of skull sutures, and the various types including plagiocephaly, scaphocephaly, and trigonocephaly. It notes treatment may involve surgery to correct skull growth abnormalities.
More Related Content
What's hot
Trigonometry - Strand 3
The document provides information about trigonometry topics for a foundation level class including: solving problems using right triangles, the Pythagorean theorem, defining trig functions like sine, cosine, and tangent for all angle values, graphing periodic trig functions like sine and cosine waves, and noting that the tangent graph has periods of 180 degrees and vertical asymptotes every 90 degrees.
Trig right triangle trig
This document provides examples and explanations of right triangle trigonometry concepts, including:
1) Finding trigonometric ratios (sine, cosine, tangent) for given angles in right triangles.
2) Using trigonometric functions to find missing side lengths, including for special 30-60-90 and 45-45-90 right triangles.
3) Applying trigonometry to real-world problems involving angles of elevation/depression and finding distances.
Reciprocal trig functions (cosecant, secant, cotangent) and the Pythagorean theorem are also discussed. Practice problems are provided to test understanding.
Solution of triangle
The document provides examples of solving right triangles using trigonometric functions. It first introduces right triangles and trigonometry. It then works through multiple examples, such as calculating the altitude of a plane given the horizontal distance traveled and angle of ascent. The examples demonstrate using trigonometric functions like tangent, cosine, and sine to solve for unknown sides and angles of right triangles based on given information.
Ks5 trigonometry
This document contains trigonometric identities and questions about trigonometric functions. It asks about the values of sin90, cos0, and which trig functions repeat every 2π radians. It also contains true/false questions about trig function equations and identities involving sin, cos, and tan. Finally, it asks which of several trig identities are correct.
11.2 Pythagorean Theorem
The document provides information about the Pythagorean theorem and right triangles:
1) It defines the key terms related to right triangles - the legs are the two sides adjacent to the right angle, and the hypotenuse is the side opposite the right angle.
2) It presents the Pythagorean theorem formula - a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
3) It provides examples of using the theorem to determine the length of missing sides of right triangles.
5 2slope
The document discusses slope and how to calculate it. It provides examples of slope in building roofs, hiking hills, and graphing linear equations. It emphasizes that slope is rise over run, where rise is the vertical change and run is the horizontal change between two points on a line. Instructions are given to find the slope of a line by taking the vertical and horizontal differences between two points and writing the ratio as a fraction.
Ms1 trig ratio
The document discusses trigonometry and using a scientific calculator to solve trigonometric problems involving right triangles. It defines the sides of a right triangle as the hypotenuse, opposite, and adjacent sides. It explains how to use the sine, cosine, and tangent functions on a calculator to find missing angles and sides of a triangle when given other information. Examples are provided for finding unknown angles from side lengths and unknown sides when given an angle measure. The document also addresses situations where the unknown value is on the bottom of a trigonometric ratio fraction.
Space diagonal lesson
(1) A space diagonal is a line that connects opposite vertices through the center of a rectangular prism.
(2) The Pythagorean theorem can be used to calculate the length of a space diagonal by treating it as the hypotenuse of a right triangle formed by the dimensions of the prism.
(3) For example, in a prism measuring 28cm by 12cm by 16cm, the space diagonal AG is calculated to be 34.4cm using the Pythagorean theorem and considering triangles ABC and ACG.
Trig overview
This document provides an overview of the six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. It defines these functions using ratios on the unit circle, and provides the value of each function at 30°, 45°, 60°, 90°, 135°, 150°, 225°, 300°, and 315° angles. It also explains that the trig functions repeat in the four quadrants of the unit circle, with the signs of x and y values changing depending on the quadrant.
OPERASI BILANGAN BULAT
Bilangan Bulat terdiri dari semua bilangan positif, nol, bilangan bulat negatif tanpa pecahan dan komponen desimal
Trig relationships
This document discusses trigonometric relationships between related angles. It contains the following rules:
1) sin(a) = sin(180 - a) and cos(a) = cos(180 - a), meaning trig functions of complementary angles are equal.
2) sin(a) = sin(-a) and cos(a) = cos(-a), meaning trig functions of coterminal angles are equal.
3) sin(a) = cos(90 - a) and cos(a) = sin(90 - a), relating trig functions that are 90 degrees out of phase.
Trigonometric Identities.
The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.
Chapter 3
This document summarizes key concepts about two-dimensional motion and vectors:
1) It introduces scalars, which have magnitude but no direction, and vectors, which have both magnitude and direction.
2) It describes methods for adding vectors graphically by drawing them as arrows and finding the resultant, or using trigonometry.
3) It explains projectile motion as objects moving under gravity with both horizontal and vertical components of motion that can be analyzed separately using kinematic equations.
Pythagorean Theorem Tutorial
This document provides a tutorial on using the Pythagorean theorem to solve for missing sides of right triangles. It explains the theorem and its formula, how to identify the sides of a right triangle, and how to solve for both missing hypotenuses and legs. Examples are worked through step-by-step and opportunities for practice are provided throughout the tutorial. The goal is for students to demonstrate mastery in solving for missing sides of right triangles.
6.1 Triangle Angle Relationships
Find the measures of missing angles of triangles
Find the measures of missing remote interior and exterior angles
Five most comprehensive examples of triangle laws
Triangle laws made simpler with these 5 comprehensive examples of Triangle law problems by Transtutors
Pythagorean Theorem Lesson
The document discusses the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It defines the key terms hypotenuse, legs, and explains the a^2 + b^2 = c^2 formula. Examples are given to demonstrate applying the theorem to find the unknown side of a right triangle given the other two sides. Practice problems are provided to reinforce the concept.
trigonometric ratio of 45
This document discusses trigonometric ratios of 450 angles. It begins by introducing trigonometry and defining types of triangles. It then specifies a right triangle with angles of 450. Through using Pythagorean theorem and the fact that two sides are equal, it derives the trigonometric ratios of sin 450, cos 450, and tan 450. Examples are also provided to demonstrate using the derived ratios. The key ratios are:
- Sin 450 = 1/√2
- Cos 450 = 1/√2
- Tan 450 = 1
Using sohcahtoa
(3) slide presentation that walks through the utilization of the SOH CAH TOA formulas, including how to plug functions into the calculator.
What's hot (19)
Viewers also liked
SCORE: strengthening student engagement
The document discusses different factors that can strengthen student engagement:
1) It identifies five main goals (Success, Curiosity, Originality, Relationships, Energy) that drive student engagement as they satisfy basic human needs.
2) For Success, it recommends clearly defining criteria for success and providing feedback to help students see skills as achievable.
3) To arouse Curiosity, it suggests providing incomplete information to compel understanding.
4) For Originality, it advises connecting creative projects to students' interests and expanding what counts as audiences.
5) Fostering Relationships involves complementary assignments and structured group work.
Pc 4.1 notes
This document discusses radians and degree measures of angles. Some key points:
- A radian is the measure of a central angle that intercepts an arc equal in length to the radius of the circle. There are 2π radians in a full circle.
- Coterminal angles have the same initial and terminal sides and can be obtained by adding or subtracting full revolutions (2π) to an angle measure.
- The document provides examples of converting between degrees and radians and finding coterminal angles.
Neural tube defects and Craniosynostosis
This document discusses various congenital anomalies that affect the central nervous system, including neural tube defects (NTDs) such as spina bifida occulta, meningocele, meningomyelocele, encephalocele, and anencephaly. It describes the embryology of neural tube formation and risk factors for NTDs such as folic acid deficiency. The document also discusses craniosynostosis, which is the premature fusion of skull sutures, and the various types including plagiocephaly, scaphocephaly, and trigonocephaly. It notes treatment may involve surgery to correct skull growth abnormalities.
Radian and degree measure.
This document discusses trigonometric functions and different ways of measuring angles. It introduces degrees and radians as units of angular measurement. Degrees are divided into minutes and seconds, with one degree equal to 1/360 of a full rotation. Radians are defined as the angle subtended by an arc of a circle whose length is equal to the radius. Some key conversions are provided, such as 1 radian being approximately 57.3 degrees and 2 pi radians equaling 360 degrees. Coterminal angles which share the same initial and terminal sides are also discussed.
Neural tube defects
Neural tube defects are caused by the abnormal closure of neural folds and can be influenced by teratogens and multifactorial genetic and environmental factors. Spina bifida is a general term used for neural tube defects in the spinal region where the vertebral arches are split apart and the underlying nervous tissue may or may not be involved. Spina bifida occulta involves a defective vertebral arch covered by skin, while spina bifida cystica features a protrusion in the form of a sac where the underlying neural tissue is involved along with the meninges. Hydrocephalus can develop in spina bifida cystica when the spinal cord is tethered to the vertebral column, pulling the cerebellum through the
Spina bifida
Spina bifida is a birth defect where the spine and spinal cord do not form properly. There are varying levels of severity, from spina bifida occulta where the defect is hidden and has no effects, to more severe cases where parts of the spinal cord and nerves bulge out from openings in the spine. This can cause problems like paralysis, loss of bladder and bowel control, and mental disabilities. Surgery is often needed right after birth to repair damage, and lifelong care involves catheterization, leg braces, and physical/mental therapy. People can help by volunteering for fundraising and awareness events.
Meningomyelocoele
Meningomyelocoele is the most severe type of spina bifida where there is a cystic swelling over the spinal defect containing meninges, nerve roots, and spinal cord outside the vertebral canal. It occurs due to failure of closure of the neural tube during development. Clinical features include lower limb paralysis, bladder and bowel dysfunction, hydrocephalus, and Arnold-Chiari malformation in 95% of cases. Treatment involves closure of the defect soon after birth along with lifelong multidisciplinary care. One study found that children with meningomyelocoele who could walk, even with aids, performed better cognitively than those who used wheelchairs, suggesting locomotion may positively impact development.
Spina Bifida presentation
Spina bifida is a birth defect that occurs when the bones of the spine do not form properly, leaving the spinal cord exposed or causing a gap in the spine. It occurs in about 1 in 1000 births and there are three main types that vary in severity from mild to severe. While the exact cause is unknown, genetic and environmental factors like obesity and diabetes in the mother may play a role. Symptoms depend on the type and severity but can include dimples or swelling on the back as well as nerve damage and paralysis in more severe cases. Treatment options vary from observation for mild cases to surgery to repair the spine for more severe types with spinal cord or nerve involvement.
Neural tube defects
Neural tube defects (NTDs) are birth defects of the brain and spinal cord that occur early in pregnancy. The most severe forms are anencephaly and rachischisis where the brain and spinal cord are exposed or absent. NTDs result from the failure of the neural tube to close properly during embryonic development. Risk factors include genetic factors and folic acid deficiency. Prenatal screening and ultrasound can detect NTDs. Treatment depends on the specific defect but may involve surgery after birth and lifelong management of complications such as hydrocephalus.
Viewers also liked (9)
Similar to Trigonometry and triangles
Trigonometry ratios in right triangle
This document discusses right triangle trigonometry. It defines the six trigonometric functions as ratios of sides of a right triangle. The sides are the hypotenuse, adjacent side, and opposite side relative to an acute angle. It shows how to calculate trig functions for a given angle and how to find an unknown angle given two sides of a right triangle using inverse trig functions. Examples are provided to demonstrate solving for missing sides and angles of right triangles using trig ratios and the Pythagorean theorem.
Trigonometry docs
This document provides an overview of trigonometry, covering right triangle trigonometry and oscillating functions. It discusses key concepts like the Pythagorean theorem, SOH CAH TOA, trig identities, and converting between degrees and radians. Right triangle trigonometry focuses on ratios of sides, while oscillating functions deal with concepts like sine, cosine, and their roles in vibrations, circuits, and calculus.
Matematika : Trapesium
The document discusses properties and calculations related to trapezoids. It defines trapezoids as shapes with four sides and four angles, with one pair of parallel sides. It provides examples of calculating the area and perimeter of various trapezoids given side lengths and heights. Examples are worked through on finding angles, areas, and perimeters of different trapezoids. Real-world objects with trapezoidal shapes like house roofs and baskets are also mentioned.
GCSE-TrigonometryOfRightAngledTriangles.pptx
This document provides an overview of trigonometry of right-angled triangles. It contains three main points:
1. It outlines objectives of finding unknown sides and angles in right-angled triangles using trigonometric ratios and inverse trigonometric functions.
2. It advertises an online resource for teaching videos, topic tests, and interactive practice questions on trigonometry organized by topic and difficulty.
3. It shares a personal anecdote of how the author first learned trigonometry and was able to apply it to write a computer program to draw an analogue clock.
Introduction to trigonometry [autosaved]
Trigonometry studies relationships involving lengths and angles of triangles. The document defines trigonometric ratios including sine, cosine, and tangent, which relate the measures of angles and sides in a right triangle. It provides examples of calculating trigonometric functions using trigonometric ratios. The document consists of several multiple choice questions testing the reader's understanding of trigonometric concepts and abilities to calculate trigonometric ratios and functions.
Triangle Trigonometry.ppt
Trigonometry deals with relationships between sides and angles in right triangles. The three main trigonometric functions are sine, cosine, and tangent, which provide ratios of sides of a right triangle based on a given angle. A scientific calculator can be used to find trigonometric ratios for any angle, as well as to calculate missing angles or sides of a right triangle when two pieces of information are known.
Pre-5.1 - trigonometry ratios in right triangle and special right triangles.ppt
Right triangle trigonometry is based on ratios of the sides of right triangles. The six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - are defined by ratios of the opposite, adjacent, and hypotenuse sides. To find a missing angle or side, the appropriate trigonometric ratio is selected based on the known sides and then calculated. There are special right triangle theorems for 45-45-90 and 30-60-90 triangles that allow determining side lengths based on one known side length.
Precalculus August 28 trigonometry ratios in right triangle and special righ...
This document discusses right triangle trigonometry. It defines the six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - which are ratios of the sides of a right triangle. The three sides are the hypotenuse, which is opposite the right angle, and the opposite and adjacent sides in relation to the acute angle. The document also provides examples of using trigonometric functions to find missing angles and sides of right triangles, including using special right triangle theorems for 45-45-90 and 30-60-90 triangles.
Geometry Test Review
The document provides a review of trigonometric ratios such as sine, cosine, and tangent that are used to solve problems involving right triangles, includes examples of applying these ratios to solve practice problems involving missing side lengths and angle measures, and discusses special right triangles and the mnemonic device SOH CAH TOA to remember the trigonometric functions.
Trigonometry, Applications of Trigonometry CBSE Class X Project
A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student
Chapter 7.pptx
This document provides learning outcomes and content from a chapter on trigonometry. The key topics covered include:
- Solving right-angled triangles using Pythagoras' theorem and trigonometric ratios
- Calculating trigonometric ratios for special angles like 30°, 45°, and 60° degrees
- Using trigonometric functions to solve practical problems involving angles of elevation and depression
- Converting between degrees and radians and graphing trigonometric functions
- Solving trigonometric equations by finding reference angles
Tangent Ratio
This document discusses the tangent ratio and how to use it to solve problems involving right triangles. It provides examples of finding the tangent of various angles, using the tangent ratio to find missing side lengths of triangles, and calculating the angle of a road given its grade. Key terms introduced are tangent ratio, sine, cosine, acute angle, opposite leg, and adjacent leg. Examples are provided to illustrate using the tangent ratio to solve problems.
Geometry Test Review
The document provides a review of trigonometric ratios such as sine, cosine, and tangent that are used to solve problems involving right triangles, includes examples of applying these ratios to solve practice problems involving missing side lengths and angle measures, and reviews special right triangles and the SOH CAH TOA method for remembering the trigonometric functions.
C2 st lecture 8 pythagoras and trigonometry handout
This document provides an overview of Pythagoras' theorem, trigonometric ratios, and formulas for working with triangles. It defines different types of triangles, introduces Pythagoras' theorem, and provides examples of using it to find missing sides of right triangles. It also defines the sine, cosine, and tangent ratios and includes examples of using trigonometric functions to find angles and sides. Finally, it presents the sine rule, cosine rule, and formulas for finding the area of various triangles.
C20 20.3
This document contains 20 questions about calculating the areas of various trapezoids. The questions provide the dimensions of the trapezoids such as lengths of the parallel and non-parallel sides and altitude. The solutions show the area calculations using the formula for the area of a trapezoid which is (sum of parallel sides) x (altitude)/2. Some questions require dividing the overall shape into geometric components like triangles, rectangles, and trapezoids to calculate the total area.
Maths Quadrilateral
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Specific types include squares, rectangles, parallelograms, rhombuses, kites, trapezoids, and cyclic quadrilaterals.
- Rectangles have opposite parallel sides of equal length and right angles. Squares are rectangles with all sides of equal length.
- Parallelograms have opposite parallel sides of equal length and opposite angles summing to 180 degrees. Rhombuses are parallelograms with all sides of equal length.
- Kites have two pairs of equal sides adjacent to each other and perpendicular diagon
Maths Quadrilateral
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Specific types include squares, rectangles, parallelograms, rhombuses, kites, trapezoids, and cyclic quadrilaterals.
- Rectangles have opposite parallel sides of equal length and right angles. Squares are rectangles with all sides of equal length.
- Parallelograms have opposite parallel sides of equal length and opposite angles summing to 180 degrees. Rhombuses are parallelograms with all sides of equal length.
- Kites have two pairs of equal sides adjacent to each other and perpendicular diagon
Maths quadrilateral presentation
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Types include squares, rectangles, parallelograms, rhombuses, kites, and trapezoids.
- Rectangles have opposite parallel sides of equal length and right angles. The perimeter of a rectangle is the sum of its sides, and its area is length multiplied by width.
- Squares are rectangles with all sides of equal length. The perimeter and area formulas are the same but use only one side length.
- Parallelograms have opposite parallel sides of equal length and opposite interior angles that sum to 180 degrees. The
Right Triangle Trigonometry
This document summarizes key concepts from a chapter on trigonometric functions. It defines the six trig functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of right triangles and provides examples of how to use trig functions to find unknown side lengths. It also introduces special right triangles used to find exact values of trig functions, such as the 45-45-90 triangle used to find sine and cosine of 45 degrees.
7.4 trigonometry -_sol_g7
This document discusses trigonometric ratios and how to use them to solve problems involving right triangles. It provides examples of calculating sine, cosine, and tangent ratios given side lengths of a right triangle. It also shows how to use a calculator to find an angle measure given a trigonometric ratio. Key ratios discussed are sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent).
Similar to Trigonometry and triangles (20)
Pre-5.1 - trigonometry ratios in right triangle and special right triangles.ppt
Pre-5.1 - trigonometry ratios in right triangle and special right triangles.ppt
Precalculus August 28 trigonometry ratios in right triangle and special righ...
Precalculus August 28 trigonometry ratios in right triangle and special righ...
Trigonometry, Applications of Trigonometry CBSE Class X Project
Trigonometry, Applications of Trigonometry CBSE Class X Project
C2 st lecture 8 pythagoras and trigonometry handout
C2 st lecture 8 pythagoras and trigonometry handout
Recently uploaded
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
PCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Leveraging Generative AI to Drive Nonprofit Innovation
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience Wahiba Chair Training & Consulting
Wahiba Chair's Talk at the 2024 Learning Ideas Conference. BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdRecently uploaded (20)
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Trigonometry and triangles
- 1. Trigonometry and Triangles Michael Schmidt
- 2. Trigonometry Sine Cosine Tangent Length of triangle legs Angle of triangle corners Area of triangles What we are doing
- 3. Branch in Mathematics Uses trig functions Triangles Mostly right triangles Uses relationships to find unknowns Trigonometry
- 4. θ (Theta) Adjacent leg (A) Opposite leg (O) Hypotenuse (H) Key Terms H O θ A
- 5. SOH: sin θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 CAH: cos θ =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 TOA: tan θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 SOH CAH TOA
- 6. sin 37° = cos37° = tan 37° = SOH CAH TOA continued 21𝑓𝑡35𝑓𝑡 28𝑓𝑡35𝑓𝑡 21𝑓𝑡28𝑓𝑡 35ft 21ft 37° 28ft
- 7. What is given? Which trig function? Finding the side length 12ft sin 30° = 𝑋12𝑓𝑡 X sin 30°1 = 𝑋12𝑓𝑡 X= 6ft 30°
- 8. Using trig, find unknown tan 20° = 𝑋6𝑚 1 X X= 2.18m 20° 6m X cos 45° = 8𝑖𝑛𝑥 1 45° X= 11.31in 8in
- 9. What is known? tan θ = 34 Use 𝑡𝑎𝑛−1 𝑡𝑎𝑛−1( 34 ) = θ θ = 36.86° Using trig to find θ 3’ θ 4’
- 10. sin θ = 10𝑚15𝑚 𝑠𝑖𝑛−1(10𝑚15𝑚 ) = θ θ = 41.81° Solve for θ θ 15m 10m cos θ = 7𝑐𝑚9𝑐𝑚 𝑐𝑜𝑠−1(7𝑐𝑚9𝑐𝑚 ) = θ θ = 38.94° 9cm θ 7cm
- 11. Area of triangle A = 𝐵𝐻2 A = 15∗102 = 75𝑚2 Finding the Area 10m 15m
- 12. What is given? What is needed? How is it found? tan60 = 𝐵10 A =17.32𝑐𝑚∗10𝑐𝑚2 Finding area with trig 60° 10cm B =17.32cm =86.6𝑐𝑚2
- 13. Given Needed sin50 = 𝐻11 A= 13∗8.432 Non right triangles H= 8.43in 11in A=54.8𝑖𝑛2 50° 13in
- 14. cos 60 = 𝐻22 Pythagorean theorem for the base A= 19.05∗112 Find area of triangle H=11in 60° 22in A=104.78𝑖𝑛2
- 15. Given Needed B= X+Y tan 45 = 𝑥16 tan 30 = 𝑦16 B=25.24cm Find area of triangle continued Height = 16cm 16cm 45° 30° X Y X=16cm Y=9.24cm A=16∗25.242 =201.92𝑐𝑚2
- 16. A 6ft tall man is standing in front of a light. The light is casting a shadow. If the angle of depression at the man’s head is 60° how long is the shadow? Story Problems tan 60 = 𝐿6 L=10.39ft 60° 6ft L
- 17. Story problems There is a window 33ft up a building and the only ladder is 40ft long. For safety reasons the ladder is leaned against the building at 52°. Will the ladder reach the window? sin 52 = 𝐻40 H=31.52ft 40ft No, the ladder will not reach the window. 52°
- 18. SOH CAH TOA is key Find the Given and Needed Make own right triangle Draw a picture Wrap up
Editor's Notes
- There is a couple ways to do the first problem. Then can use Pythagorean theorem.