March 19 Trig Review
•
0 likes•641 views
Trigonometry is used to determine the measures (sides and angles) of a right triangle. The document reviews three trigonometric functions: sine, cosine, and tangent. Sine relates an angle to the opposite side over the hypotenuse. Cosine relates an angle to the adjacent side over the hypotenuse. Tangent relates an angle to the opposite side over the adjacent side. An example problem is shown to find missing sides and angles of a right triangle when given one angle measure and the side opposite to it.
Report
Share
Report
Share
Download to read offline
Recommended
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.
Triginometry
The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.
Grade 10 Trig.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The cosine law can be used to find missing side lengths or angles in any triangle where two sides and the angle between them are known. The sine law relates the sines of the angles of a triangle to the lengths of the sides opposite them.
Law of sine and cosines
This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.
sine and cosine rule
- The Sine Rule and Cosine Rule can be used to find unknown sides and angles in triangles that are not right-angled.
- The Sine Rule states that the ratio of the sine of an angle to its opposite side is equal to the ratio of any other angle-side pair. It is generally easier to use than the Cosine Rule.
- The Cosine Rule relates all three sides of a triangle to one of its interior angles. It can be used to find a single unknown when three other parts of the triangle are known.
Law Of Sines; Powerpoint
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.
Sine rule
The sine rule can be used to solve for unknown sides or angles of any triangle when enough information is given, such as two sides and the angle between them, or one side and two angles. It relates the ratios of sides to opposite angles: a/sinA = b/sinB = c/sinC. To use it, corresponding sides and angles are matched up and the ratios set equal. Then cross-multiplication and inverse trigonometric functions are used to solve for the unknown. Worked examples show how to calculate missing sides or angles.
Law of Sines notes
The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides the Law of Sines formula that relates the ratios of sides to opposite angles. It gives two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It also provides the formula to find the area of a triangle using two sides and the included angle. Several example problems are worked through applying the Law of Sines to find missing side lengths and triangle areas.
Recommended
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.
Triginometry
The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.
Grade 10 Trig.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The cosine law can be used to find missing side lengths or angles in any triangle where two sides and the angle between them are known. The sine law relates the sines of the angles of a triangle to the lengths of the sides opposite them.
Law of sine and cosines
This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.
sine and cosine rule
- The Sine Rule and Cosine Rule can be used to find unknown sides and angles in triangles that are not right-angled.
- The Sine Rule states that the ratio of the sine of an angle to its opposite side is equal to the ratio of any other angle-side pair. It is generally easier to use than the Cosine Rule.
- The Cosine Rule relates all three sides of a triangle to one of its interior angles. It can be used to find a single unknown when three other parts of the triangle are known.
Law Of Sines; Powerpoint
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.
Sine rule
The sine rule can be used to solve for unknown sides or angles of any triangle when enough information is given, such as two sides and the angle between them, or one side and two angles. It relates the ratios of sides to opposite angles: a/sinA = b/sinB = c/sinC. To use it, corresponding sides and angles are matched up and the ratios set equal. Then cross-multiplication and inverse trigonometric functions are used to solve for the unknown. Worked examples show how to calculate missing sides or angles.
Law of Sines notes
The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides the Law of Sines formula that relates the ratios of sides to opposite angles. It gives two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It also provides the formula to find the area of a triangle using two sides and the included angle. Several example problems are worked through applying the Law of Sines to find missing side lengths and triangle areas.
Trigonometry
The document discusses trigonometry and its key concepts. It defines trigonometry as the study of relationships between sides and angles of triangles. It then covers right triangles, trigonometric ratios, the Pythagorean theorem, and ratios for common angles like 45, 60, and 90 degrees. Key formulas discussed include sine, cosine, tangent, cotangent, secant, and cosecant. Relationships between the ratios are also summarized.
Law of Cosines
The Law of Cosines is an equation that can be used to find the length of any side of a triangle if two sides and the angle between them are known. It is more versatile than the Pythagorean theorem, which only applies to right triangles. The Law of Cosines states: c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C. Several examples are provided to demonstrate using the Law of Cosines to calculate lengths and angles of triangles. Variations of the equation allow solving for a, b, or the angles instead of c.
Trigo the sine and cosine rule
This document provides information on solving triangular problems using the sine and cosine rules. It explains that the sine rule can be used to calculate sides and angles in triangles where there is no right angle when two angles and a side or two sides and a non-included angle are known. Examples are provided to demonstrate using the sine rule to find missing sides and angles. The cosine rule is introduced as another method that can be used when three sides are known or two sides and an included angle. Examples demonstrate using the cosine rule to find a missing side or angle.
Oblique triangles made by: MR. ROLAND M. LEOPAR
This document discusses oblique triangles and the sine law and cosine law for solving triangles. It provides examples of applying these laws to find missing angles and sides of triangles given various parts of triangles, such as two sides and the included angle, two angles and the included side, or three sides. The seven examples show step-by-step workings of applying the sine and cosine laws to find the missing parts in different triangle scenarios.
Sine and cosine rule
The document provides guidance on using trigonometric rules to solve problems involving sides and angles of triangles. It explains that the Sine Rule is used when there is a "matching pair" of a known side and its corresponding angle. The Cosine Rule is used when there is no right angle or matching pair. Examples are given of using both rules to calculate missing sides or angles of triangles.
Trignometry and Its Importance for Class 10
this is a trigonometry ppt or slide made for my class 10 individual project . Hope you will enjoy this.
Obj. 43 Laws of Sines and Cosines
The document discusses two trigonometric identities, the Law of Sines and the Law of Cosines, that can be used to solve for unknown sides and angles in any triangle when sufficient information is given. The Law of Sines relates the ratios of the sines of the angles to the lengths of the sides opposite those angles. The Law of Cosines relates all three sides of a triangle and the angle opposite one of the sides. Examples are provided to demonstrate solving problems using each law.
Angles
An angle is formed by two rays with a common endpoint called the vertex. Angles are measured in degrees and can be acute, right, obtuse, straight, or reflex depending on their measure. The protractor postulate allows pairing angles with degree measures between 0 and 180 degrees. The angle addition postulate states that if a point is within an angle, the measures of the angles on either side of it will sum to the total angle measure. Adjacent angles share a vertex and side, complementary angles sum to 90 degrees, and vertical angles are opposite angles formed by two lines and are congruent.
4th l6. oblique triangle
Here are the steps to solve this problem:
a. AC is the hypotenuse of the right triangle ABC.
We are given that AB = 6 units
and angle BAC = 45 degrees
Using the trigonometric identity that sin(45) = 0.5, we can set up:
sin(45) = opposite/hypotenuse
0.5 = AB/AC
AC = AB/sin(45)
AC = 6/0.5 = 12 units
b. To find BC, we can use the Pythagorean theorem since this is a right triangle:
BC^2 = AB^2 + AC^2 - 2AB*ACcos(B)
BC
Matematicas1.pptx convertido
1. Given a triangle ABC where angle B measures 75° and side BC measures 6 cm, calculate the length of side AC if angle A measures 21°.
2. Given triangle ABC where a = 9 cm, c = 7 cm, and angle B = 35°, calculate the length of side b.
3. Given triangle ABC where a = 5 cm, angle A = 74.3°, angle B = 90°, and angle C = 15.7°, calculate the length of side c.
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.
Trigonometry: Solving Triangles
The document summarizes two laws for solving triangles - the Law of Cosines and the Law of Sines. It also discusses an ambiguous case of the Law of Sines. The Law of Cosines can be used to find a missing side given two sides and the included angle, or to find a missing angle given all three sides. The Law of Sines can be used to find a missing side or angle given two angles and the side opposite one of them. The ambiguous case allows finding a missing angle given two sides and the angle opposite one of them.
Trignometry
This document provides an overview of trigonometry including:
- Definitions of angles, arc length, and conversions between degrees and radians
- Right triangle trigonometric definitions of sine, cosine, tangent and their inverses
- Properties of special right triangles with angles of 30, 45, and 60 degrees
- Basic trigonometric identities involving quotient, even/odd, and reciprocal functions
- Signs of trigonometric functions in the different quadrants on the unit circle
A) proving angle properties of circles 2
This document proves the angle property that the angle subtended by an arc at the center of a circle is twice the angle subtended at the circumference. It provides an alternative proof for when a line cannot be drawn through the center and both angles. It does this by extending one arc line to the center, using properties of isosceles triangles and exterior angles to set up an equation relating the angles, and solving the equation to prove the property.
Hprec10 1
The document discusses the Law of Cosines, which extends trigonometry to non-right triangles. It defines the Law of Cosines using three equations relating the sides and angles of a triangle. Examples are provided to demonstrate solving for missing sides and angles of triangles using the Law of Cosines given various known values.
8.4 the law of cosines
The Law of Cosines is used to calculate the length of one side of a triangle when two sides and the included angle are known, or when all three sides are known. It states that the square of one side of a triangle equals the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.
00214
Trigonometry uses sine and cosine curves to relate angles and sides of triangles. The sine rule uses sine values to calculate sides of any triangle based on angles, while the cosine rule uses cosine to calculate sides based on one angle and the other two sides, without needing a right angle. Trigonometry allows calculating unknown values in triangles beyond just right triangles.
trigonometry
1. Draw two right triangles sharing the hypotenuse of 45m
2. For the first triangle, use tan to find the height of building A as 77.94m
3. For the second triangle, use tan to find the height of building B
Oblique triangles
The document discusses trigonometric methods for solving oblique triangles. It defines sine law as relating each side of a triangle to the sine of its opposite angle. Sine law is used when the given data includes a side and its opposite angle. Cosine law defines the square of any side as the sum of the squares of the other two sides minus twice the product of those sides times the cosine of the angle between them. Cosine law can be used to solve for any side or angle of a triangle given the other two sides and their included angle.
Quadratic Functions Min Max
The maximum area for Betty's garden is 156.25 sq meters when each side is 12.5 meters long. This is found by modeling the problem with the equations:
2L + 2W = 50
MAX = LW
Solving the equations gives L = W = 12.5 meters.
March 19 Trig With 2 Triangles
This document contains information about two triangles used to solve for the length of line BD. Triangle ABC has angles of 30, 42, and 50 degrees and triangle ACD has angles of 35, 56, and 36 degrees. The problem is asking to use the information provided to calculate the length of line CD.
More Related Content
What's hot
Trigonometry
The document discusses trigonometry and its key concepts. It defines trigonometry as the study of relationships between sides and angles of triangles. It then covers right triangles, trigonometric ratios, the Pythagorean theorem, and ratios for common angles like 45, 60, and 90 degrees. Key formulas discussed include sine, cosine, tangent, cotangent, secant, and cosecant. Relationships between the ratios are also summarized.
Law of Cosines
The Law of Cosines is an equation that can be used to find the length of any side of a triangle if two sides and the angle between them are known. It is more versatile than the Pythagorean theorem, which only applies to right triangles. The Law of Cosines states: c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C. Several examples are provided to demonstrate using the Law of Cosines to calculate lengths and angles of triangles. Variations of the equation allow solving for a, b, or the angles instead of c.
Trigo the sine and cosine rule
This document provides information on solving triangular problems using the sine and cosine rules. It explains that the sine rule can be used to calculate sides and angles in triangles where there is no right angle when two angles and a side or two sides and a non-included angle are known. Examples are provided to demonstrate using the sine rule to find missing sides and angles. The cosine rule is introduced as another method that can be used when three sides are known or two sides and an included angle. Examples demonstrate using the cosine rule to find a missing side or angle.
Oblique triangles made by: MR. ROLAND M. LEOPAR
This document discusses oblique triangles and the sine law and cosine law for solving triangles. It provides examples of applying these laws to find missing angles and sides of triangles given various parts of triangles, such as two sides and the included angle, two angles and the included side, or three sides. The seven examples show step-by-step workings of applying the sine and cosine laws to find the missing parts in different triangle scenarios.
Sine and cosine rule
The document provides guidance on using trigonometric rules to solve problems involving sides and angles of triangles. It explains that the Sine Rule is used when there is a "matching pair" of a known side and its corresponding angle. The Cosine Rule is used when there is no right angle or matching pair. Examples are given of using both rules to calculate missing sides or angles of triangles.
Trignometry and Its Importance for Class 10
this is a trigonometry ppt or slide made for my class 10 individual project . Hope you will enjoy this.
Obj. 43 Laws of Sines and Cosines
The document discusses two trigonometric identities, the Law of Sines and the Law of Cosines, that can be used to solve for unknown sides and angles in any triangle when sufficient information is given. The Law of Sines relates the ratios of the sines of the angles to the lengths of the sides opposite those angles. The Law of Cosines relates all three sides of a triangle and the angle opposite one of the sides. Examples are provided to demonstrate solving problems using each law.
Angles
An angle is formed by two rays with a common endpoint called the vertex. Angles are measured in degrees and can be acute, right, obtuse, straight, or reflex depending on their measure. The protractor postulate allows pairing angles with degree measures between 0 and 180 degrees. The angle addition postulate states that if a point is within an angle, the measures of the angles on either side of it will sum to the total angle measure. Adjacent angles share a vertex and side, complementary angles sum to 90 degrees, and vertical angles are opposite angles formed by two lines and are congruent.
4th l6. oblique triangle
Here are the steps to solve this problem:
a. AC is the hypotenuse of the right triangle ABC.
We are given that AB = 6 units
and angle BAC = 45 degrees
Using the trigonometric identity that sin(45) = 0.5, we can set up:
sin(45) = opposite/hypotenuse
0.5 = AB/AC
AC = AB/sin(45)
AC = 6/0.5 = 12 units
b. To find BC, we can use the Pythagorean theorem since this is a right triangle:
BC^2 = AB^2 + AC^2 - 2AB*ACcos(B)
BC
Matematicas1.pptx convertido
1. Given a triangle ABC where angle B measures 75° and side BC measures 6 cm, calculate the length of side AC if angle A measures 21°.
2. Given triangle ABC where a = 9 cm, c = 7 cm, and angle B = 35°, calculate the length of side b.
3. Given triangle ABC where a = 5 cm, angle A = 74.3°, angle B = 90°, and angle C = 15.7°, calculate the length of side c.
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.
Trigonometry: Solving Triangles
The document summarizes two laws for solving triangles - the Law of Cosines and the Law of Sines. It also discusses an ambiguous case of the Law of Sines. The Law of Cosines can be used to find a missing side given two sides and the included angle, or to find a missing angle given all three sides. The Law of Sines can be used to find a missing side or angle given two angles and the side opposite one of them. The ambiguous case allows finding a missing angle given two sides and the angle opposite one of them.
Trignometry
This document provides an overview of trigonometry including:
- Definitions of angles, arc length, and conversions between degrees and radians
- Right triangle trigonometric definitions of sine, cosine, tangent and their inverses
- Properties of special right triangles with angles of 30, 45, and 60 degrees
- Basic trigonometric identities involving quotient, even/odd, and reciprocal functions
- Signs of trigonometric functions in the different quadrants on the unit circle
A) proving angle properties of circles 2
This document proves the angle property that the angle subtended by an arc at the center of a circle is twice the angle subtended at the circumference. It provides an alternative proof for when a line cannot be drawn through the center and both angles. It does this by extending one arc line to the center, using properties of isosceles triangles and exterior angles to set up an equation relating the angles, and solving the equation to prove the property.
Hprec10 1
The document discusses the Law of Cosines, which extends trigonometry to non-right triangles. It defines the Law of Cosines using three equations relating the sides and angles of a triangle. Examples are provided to demonstrate solving for missing sides and angles of triangles using the Law of Cosines given various known values.
8.4 the law of cosines
The Law of Cosines is used to calculate the length of one side of a triangle when two sides and the included angle are known, or when all three sides are known. It states that the square of one side of a triangle equals the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.
00214
Trigonometry uses sine and cosine curves to relate angles and sides of triangles. The sine rule uses sine values to calculate sides of any triangle based on angles, while the cosine rule uses cosine to calculate sides based on one angle and the other two sides, without needing a right angle. Trigonometry allows calculating unknown values in triangles beyond just right triangles.
trigonometry
1. Draw two right triangles sharing the hypotenuse of 45m
2. For the first triangle, use tan to find the height of building A as 77.94m
3. For the second triangle, use tan to find the height of building B
Oblique triangles
The document discusses trigonometric methods for solving oblique triangles. It defines sine law as relating each side of a triangle to the sine of its opposite angle. Sine law is used when the given data includes a side and its opposite angle. Cosine law defines the square of any side as the sum of the squares of the other two sides minus twice the product of those sides times the cosine of the angle between them. Cosine law can be used to solve for any side or angle of a triangle given the other two sides and their included angle.
What's hot (20)
Viewers also liked
Quadratic Functions Min Max
The maximum area for Betty's garden is 156.25 sq meters when each side is 12.5 meters long. This is found by modeling the problem with the equations:
2L + 2W = 50
MAX = LW
Solving the equations gives L = W = 12.5 meters.
March 19 Trig With 2 Triangles
This document contains information about two triangles used to solve for the length of line BD. Triangle ABC has angles of 30, 42, and 50 degrees and triangle ACD has angles of 35, 56, and 36 degrees. The problem is asking to use the information provided to calculate the length of line CD.
Lesson 18: Maximum and Minimum Values (handout)
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Lesson 18: Maximum and Minimum Values (Section 041 slides)
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Lesson 19: Maximum and Minimum Values
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
Maximums and minimum
Applications of maximums and minimums in Calculus. This includes infection points, critical points, increasing and decreasing, etc.
March 19 Quadratic Test Review
The function is a quadratic function in the form f(x) = ax2 + bx + c, with a = 2, b = -4, and c = -1. It has a vertex of (1, -3), an axis of symmetry at x = 1, a domain of all real numbers, and a range of [-3,∞). The y-intercept is -1 and the x-intercepts (roots) are 1 ± 0.5√6.
Viewers also liked (7)
Lesson 18: Maximum and Minimum Values (Section 041 slides)
Lesson 18: Maximum and Minimum Values (Section 041 slides)
Similar to March 19 Trig Review
Triginometry
The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.
Assignment # 4
This module introduces triangle trigonometry and solving for unknown sides and angles of right triangles. It provides 5 lessons:
1. Determining the appropriate trigonometric equation based on the given information in a right triangle.
2. Solving right triangles when given the hypotenuse and one leg.
3. Solving right triangles when given the hypotenuse and one acute angle.
4. Solving right triangles when given one leg and one acute angle.
5. Solving right triangles when given the measures of both legs. It includes examples and practice problems for each case.
Putter King Education - Math (Level 3)
Area of focus: Trigonometry and mathematical proofs
Topics covered:
> Trigonometry
> Right triangle definitions
> Trigonometric functions
> Special right triangles
> Law of sines
> Law of cosines
> Postulates and axioms
> Theorems
> Pythagorean Theorem
> Mathematical proof
Suggested time to complete (2 hrs):
> Teaching material (40 minutes)
> Practice activity (20 minutes)
> Final project (60 minutes)
Trigonometry
The document discusses trigonometric functions of an acute angle in a right triangle. It defines the six trig functions (sine, cosine, tangent, cotangent, secant, cosecant) in terms of the sides of the right triangle. It then gives an example of calculating the trig functions of angle A in a right triangle where the lengths of sides a and b are given.
นำเสนอตรีโกณมิติจริง
Trigonometry deals with relationships between the sides and angles of triangles, especially right triangles. It has many applications in fields like astronomy, architecture, engineering, and more. The document provides examples of using trigonometric functions like sine, cosine, and tangent to solve problems involving right triangles, including finding unknown side lengths and angles. It also discusses various trigonometric identities and applications of trigonometry in areas like digital imaging, waves, and architecture.
นำเสนอตรีโกณมิติจริง
Trigonometry is the branch of mathematics that deals with relationships between the sides and angles of triangles, especially right triangles. It studies functions of angles called trigonometric functions, including sine, cosine, and tangent. Trigonometry has applications in calculating lengths and angles without direct measurement, and was originally developed to solve problems in fields like astronomy, surveying, and navigation.
Module 1 triangle trigonometry
This module introduces triangle trigonometry and solving for unknown sides and angles of right triangles. It covers determining the appropriate trigonometric function to use given known parts of a right triangle, such as the hypotenuse and one leg. Examples are provided to demonstrate applying trigonometric functions like sine, cosine, and tangent to find missing lengths and angles. The module also addresses solving right triangle problems involving angles of elevation and depression that are commonly seen in fields like surveying.
l1. trigonometric function
This document discusses trigonometric ratios and their use in solving for missing sides and angles of right triangles. It provides examples of using trigonometric ratios like sine, cosine, and tangent to find values of angles and sides when given information about two sides of a right triangle. It also includes practice problems where the learner must use trigonometric functions on a calculator to determine values. Overall, the document aims to teach learners how to apply the six trigonometric ratios to solve for unknown values in right triangles.
Ppt on trignomentry
This document discusses trigonometric ratios and identities. It defines the trigonometric ratios of sine, cosine and tangent for an acute angle A in a right triangle ABC. It also defines cosecant, secant and cotangent. It provides the reciprocal identities and values of the trigonometric ratios for common angles. It lists formulas for trigonometric functions of complementary angles and the main trigonometric identities along with steps for proving identities.
Yogie.pptx trigonometry kvs
The PowerPoint presentation is on the "BASICS OF TRIGONOMETRY".
It includes the --
1) Definition of Trigonometry,
2) History of Trigonometry and its Etymology,
3) Angles of a Right Triangle,
4) About different Trigonometric Ratios,
5) Some useful Mnemonics to remember the Trig. ratios,
6) Theorem, which states that --
"Trigonometric Ratios are same for the same angles"
7) Trigonometric Ratios for some specific/ standard angles.
Unidad 2 pensamiento variaciones y trigonométrico:ley del seno
This document defines trigonometric functions using right triangles and explains the Law of Sines. It gives definitions for sine, cosine, tangent, cosecant, and secant in terms of the sides of a right triangle and associated angles. It then presents an example problem using the Law of Sines to solve for the measures of an unknown side and angle of a triangle given the measures of two sides and one angle. The example finds the missing side to be 11.54 meters.
Assignment # 5
This module discusses solving oblique triangles using the law of sines. It begins by introducing acute and obtuse triangles and how to find the measure of the third angle given two angles. It then derives the law of sines and shows how it can be used to solve triangles where two angles and a side opposite one angle are given, two angles and the included side are given, or all three sides are given. Examples of solving various triangle scenarios are provided.
INTRODUCTION TO TRIGNOMETRY ppt
Trigonometry is the combined Maths of geometry and algebra, deals with the relationships between the sides and angles of a right angled triangle.
14 right angle trigonometry
This document provides information on right triangle trigonometry including definitions of basic angle types, right triangle properties, the Pythagorean theorem, trigonometric ratios, and how to solve right triangle problems. It defines trigonometric functions like sine, cosine, and tangent in terms of an acute angle and adjacent/opposite sides. Examples are given for finding missing side lengths and converting between angle units. Practice problems apply the concepts to evaluate trig functions and solve application problems involving heights, distances, and angles of elevation/depression.
Trignometry
This document provides an introduction to trigonometry, including definitions of key terms like hypotenuse, perpendicular, and base in the context of a right triangle. It explains Pythagoras' theorem that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. Trigonometric ratios like sine, cosine, and tangent are also defined in terms of the sides of a right triangle. An example problem demonstrates using trigonometric ratios and Pythagoras' theorem to solve for a missing side of a triangle.
Trigonometric ratios
The concept of trigonometric ratios is important in Maths trigonometry. Some of applications and procedures are discussed here for easy understanding the concept clarity.
Basic trigonometry ideas
This document introduces basic trigonometry concepts including:
- The parts of a right triangle - adjacent side, opposite side, and hypotenuse.
- How to identify the adjacent and opposite sides depending on the angle being considered.
- The three basic trigonometric ratios - sine, cosine, and tangent - defined in terms of the sides of a right triangle.
- The mnemonic device "SOHCAHTOA" for remembering the ratios.
- Examples showing how to calculate the trig ratios for angles in right triangles.
- How trig ratios are the same for similar triangles since corresponding angles are equal.
Lesson exemplar in writing the equation needed in solving the right triangle
The document provides a lesson on solving right triangles using trigonometric ratios. It begins by reviewing the parts of a right triangle, including the legs and hypotenuse. It then defines the six trigonometric ratios using sine, cosine, tangent, cosecant, secant, and cotangent. Examples are provided to demonstrate determining the appropriate ratio to use when a right triangle has given and missing parts. Students are assessed on writing the correct formula to solve for missing parts in various right triangle scenarios.
L1 Terms Ratios Find Missing Side
This document provides an overview of trigonometric ratios and how to use them to solve problems involving right triangles. It defines the sine, cosine, and tangent ratios and provides the mnemonic device SOH CAH TOA to remember them. Examples are given of calculating trig ratios in right triangles and using them to solve application problems like finding the length of a ladder leaning against a wall.
Similar to March 19 Trig Review (20)
Unidad 2 pensamiento variaciones y trigonométrico:ley del seno
Unidad 2 pensamiento variaciones y trigonométrico:ley del seno
Lesson exemplar in writing the equation needed in solving the right triangle
Lesson exemplar in writing the equation needed in solving the right triangle
More from ste ve
March 17 Chequebook Recod
You start with $400 in your chequing account. On March 18 you deposit a $300 paycheck, bringing your balance to $700. On March 19 you write 4 cheques: cheque #22 for $45 to Manitoba Hydro, cheque #23 for $55 to the City of Winnipeg, cheque #24 for $200 to Visa, and cheque #25 for $50 to DMCI, reducing your balance to $350.
March 18 Reconciliation
Reconciling a bank statement involves comparing transaction records to the bank's statement to identify any differences. When reconciling, the reconciler finds transactions recorded by one party but not the other. By accounting for these differences in a reconciliation statement, the reconciler can ensure the final balances match and identify any potential errors made by either party. The process involves listing matching transactions, recording the initial balances, then adding deposits or subtracting withdrawals found in one record but not the other to make the final balances equal. If the balances do not match after reconciliation, an error has occurred that requires correction.
March 18 Radicals
This document discusses square roots and their properties. It provides examples of taking the square root of both sides of an equation to solve for the variable. It also shows combining like terms within square root expressions and then taking the square root of both sides to isolate the variable.
March 18 Withdrawal Slips
Withdrawal slips are records of when and how much money is taken out of a bank account. The document instructs the reader to fill out a sample withdrawal slip pretending to withdraw $100 from their account on the current date. The slip would document the pretend $100 withdrawal for record keeping purposes.
March 18 Compound Interest
The document discusses compound interest rates across three scenarios. In the first, investing $1000 at 8% interest compounded semi-annually for 4 years would yield more than the original $1000. In the second, Jim's Bank offering 6% interest compounded monthly on deposits over $2000 is a better choice than Steve's Bank offering 5% compounded weekly, if the money is left for 2 years. In the third, Peter buys a $500 laptop on a credit card with 17.5% interest compounded monthly but cannot pay for 6 months, making the real cost of the laptop more than $500.
March 17 Rule Of 72
The document discusses the rule of 72, which is a method for estimating how long it will take an investment to double in value at a given annual interest rate. It states that to estimate the number of years for an investment to double, one should divide 72 by the annual interest rate percentage. However, the document provides no further explanation or context regarding the rule of 72.
March 16 Compound Interest 2
The document discusses compound interest rates and calculations. It asks how much money would be earned from investing $1000 at 8% interest compounded semi-annually over 4 years. It also asks which bank would earn more interest over 2 years, between one offering 6% interest compounded monthly on deposits over $2000, and another offering 5% interest compounded weekly on the same size deposits.
March 12 Forms Of Lines
There are three forms of lines: slope-intercept form (y=mx+b), standard form (ax+by+c=0), and neither of the above. Slope-intercept form provides the slope and y-intercept in a simple way. Standard form writes the line as a polynomial with everything on one side of the equation and x positive. Standard form can be found by converting slope-intercept form or by knowing two points that the line passes through.
March 12 Discriminant
The document discusses the discriminant of a quadratic equation and what the sign of the discriminant indicates about the number of roots. It provides an example quadratic equation of 4x^2 + 3x + 8 = 0. It then shows:
1) Calculating the discriminant of -119 which is negative, indicating there are no real roots.
2) A general explanation that a negative discriminant means no real roots, while a positive discriminant means there are two real roots.
3) When the discriminant is 0, there is exactly one real root.
March 11 Deposit Slips
This document provides instructions for completing deposit slips based on sample transactions. It describes that a deposit slip records money deposited into a bank account. It gives an example of Betty depositing two cheques for $30 and $40, as well as $40 in cash and $4 in coins. It also provides an example for Steve depositing three cheques for $35, $47, and $25.67 and taking $40 in cash from the deposit. The document aims to demonstrate how to fill out deposit slips.
March 9 Quadratic Formula
The quadratic formula provides a method to solve quadratic equations of the form ax^2 + bx + c = 0. It expresses the solutions for x in terms of the coefficients a, b, and c as x = (-b ± √(b^2 - 4ac))/2a. The document demonstrates applying the quadratic formula to solve the equation 7x^2 + 14x - 3 = 0, obtaining the two solutions x1 = 0.2 and x2 = -2.2.
March 9 Determing Equations
The document provides examples of determining the equation of a line given information about its slope and a point it passes through. It works through four examples, finding the equation of a line with slope 7 and y-intercept -4, slope -4/5 passing through (1,3), slope 2/3 passing through (8,1), and slope 1/9 passing through (-2,5). The examples demonstrate how to set up and solve systems of equations to determine the y-intercept and write the equation in y=mx+b form.
March 9 Determing Equations
The document provides examples of determining the equation of a line given information about its slope and a point it passes through. It works through four examples, finding the equation of a line with slope 7 and y-intercept -4, slope -4/5 passing through (1,3), slope 2/3 passing through (8,1), and slope 1/9 passing through (-2,5). The examples demonstrate how to set up and solve systems of equations to determine the y-intercept and write the equation in y=mx+b form.
March 9 Quadratic Formula
The quadratic formula provides a method to solve quadratic equations of the form ax^2 + bx + c = 0. It expresses the solutions for x in terms of the coefficients a, b, and c as x = (-b ± √(b^2 - 4ac))/2a. The document demonstrates applying the quadratic formula to solve the equation 7x^2 + 14x - 3 = 0, obtaining the two solutions x1 = 0.2 and x2 = -2.2.
March 9 Ex 12
This document appears to be an exercise labeled as number 12. No other context or details are provided about the nature or content of the exercise. The single word "Exercise 12" is the only information given in the document.
March 8 Compound Interest
The document explains compound interest using examples of borrowing $1000 at 8% interest for 1 year, and then not paying it back for additional years. It shows how the interest builds on itself each year, with the borrower paying interest on accumulated interest. A formula is provided to calculate the final amount for any principal, interest rate, number of compounding periods per year, and term of years. An example calculates the amount owed after 2 years at 6% interest compounded semi-annually.
Ambiguous Case1
The document discusses the sine and cosine laws for solving triangles. It provides examples of using these laws to calculate missing angles and sides of triangles when given certain information. However, one of the examples leads to two possible triangle solutions, showing that the information provided an ambiguous case with multiple valid options. The summary concludes that without more context, both triangle solutions are considered correct since the given information allows for more than one possibility.
March 4 Pay Raise
This document discusses pay raises and how to calculate new salaries after a percentage increase. It provides two examples: one where Joan received an 8% raise on her $1000 monthly salary, increasing it to $1080, and another where Steve's $45,000 annual salary was increased 15% to $51,750 after his raise. Percentage raises are commonly used to increase employee salaries over time based on a set percentage of their current pay.
March 8 Quadratic Equations
This document defines key terms related to quadratic equations such as monomial, binomial, trinomial, and polynomial. It explains that a quadratic equation is a polynomial of the form ax^2 + bx + c = 0, which can be graphed as a parabola. The roots or zeros of a quadratic equation are the values of x where the equation equals 0. As an example, it finds the roots of the quadratic equation x^2 + 5x + 6 = 0 to be -2 and -3.
March 8 Pay Raise 2
This document provides examples of calculating percentage pay raises based on starting salary and new salary amounts. It first shows an example of calculating an 8% raise on a $10 hourly wage. It then gives an example of determining the percentage increase for an employee who received a $60 weekly raise on a $500 weekly wage, which is a 12% raise. The final example shows calculating an 8.333% raise for an employee whose annual pay will increase from $60,000 to $65,000.
More from ste ve (20)
Recently uploaded
Promoting Wellbeing - Applied Social Psychology - Psychology SuperNotes
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
share - Lions, tigers, AI and health misinformation, oh my!.pptx
• Pitfalls and pivots needed to use AI effectively in public health
• Evidence-based strategies to address health misinformation effectively
• Building trust with communities online and offline
• Equipping health professionals to address questions, concerns and health misinformation
• Assessing risk and mitigating harm from adverse health narratives in communities, health workforce and health system
Does Over-Masturbation Contribute to Chronic Prostatitis.pptx
In some case, your chronic prostatitis may be related to over-masturbation. Generally, natural medicine Diuretic and Anti-inflammatory Pill can help mee get a cure.
Top 10 Best Ayurvedic Kidney Stone Syrups in India
we have mentioned the best 10 ayurvedic Kidney Stone Syrups. You can check all these products and choose the best one for yourself.
Hemodialysis: Chapter 4, Dialysate Circuit - Dr.Gawad
- Video recording of this lecture in English language: https://youtu.be/kqbnxVAZs-0
- Video recording of this lecture in Arabic language: https://youtu.be/SINlygW1Mpc
- Link to download the book free: https://nephrotube.blogspot.com/p/nephrotube-nephrology-books.html
- Link to NephroTube website: www.NephroTube.com
- Link to NephroTube social media accounts: https://nephrotube.blogspot.com/p/join-nephrotube-on-social-media.html
Role of Mukta Pishti in the Management of Hyperthyroidism
Muktapishti is a traditional Ayurvedic preparation made from Shoditha Mukta (Purified Pearl), is believed to help regulate thyroid function and reduce symptoms of hyperthyroidism due to its cooling and balancing properties. Clinical evidence on its efficacy remains limited, necessitating further research to validate its therapeutic benefits.
8 Surprising Reasons To Meditate 40 Minutes A Day That Can Change Your Life.pptx
8 Surprising Reasons To Meditate 40 Minutes A Day That Can Change Your Life.pptxHolistified Wellness
We’re talking about Vedic Meditation, a form of meditation that has been around for at least 5,000 years. Back then, the people who lived in the Indus Valley, now known as India and Pakistan, practised meditation as a fundamental part of daily life. This knowledge that has given us yoga and Ayurveda, was known as Veda, hence the name Vedic. And though there are some written records, the practice has been passed down verbally from generation to generation.Part II - Body Grief: Losing parts of ourselves and our identity before, duri...
Learn about body grief and ways to cope with it. We will also explore methods to heal from this challenging experience.
Journal Article Review on Rasamanikya
Rasamanikya is a excellent preparation in the field of Rasashastra, it is used in various Kushtha Roga, Shwasa, Vicharchika, Bhagandara, Vatarakta, and Phiranga Roga. In this article Preparation& Comparative analytical profile for both Formulationon i.e Rasamanikya prepared by Kushmanda swarasa & Churnodhaka Shodita Haratala. The study aims to provide insights into the comparative efficacy and analytical aspects of these formulations for enhanced therapeutic outcomes.
Integrating Ayurveda into Parkinson’s Management: A Holistic Approach
Explore the benefits of combining Ayurveda with conventional Parkinson's treatments. Learn how a holistic approach can manage symptoms, enhance well-being, and balance body energies. Discover the steps to safely integrate Ayurvedic practices into your Parkinson’s care plan, including expert guidance on diet, herbal remedies, and lifestyle modifications.
Basavarajeeyam - Ayurvedic heritage book of Andhra pradesh
Basavarajeeyam is an important text for ayurvedic physician belonging to andhra pradehs. It is a popular compendium in various parts of our country as well as in andhra pradesh. The content of the text was presented in sanskrit and telugu language (Bilingual). One of the most famous book in ayurvedic pharmaceutics and therapeutics. This book contains 25 chapters called as prakaranas. Many rasaoushadis were explained, pioneer of dhatu druti, nadi pareeksha, mutra pareeksha etc. Belongs to the period of 15-16 century. New diseases like upadamsha, phiranga rogas are explained.
Novas diretrizes da OMS para os cuidados perinatais de mais qualidade
Novas diretrizes da OMS para os cuidados perinatais de mais qualidadeProf. Marcus Renato de Carvalho
Recomendações da OMS sobre cuidados maternos e neonatais para uma experiência pós-natal positiva.
Em consonância com os ODS – Objetivos do Desenvolvimento Sustentável e a Estratégia Global para a Saúde das Mulheres, Crianças e Adolescentes, e aplicando uma abordagem baseada nos direitos humanos, os esforços de cuidados pós-natais devem expandir-se para além da cobertura e da simples sobrevivência, de modo a incluir cuidados de qualidade.
Estas diretrizes visam melhorar a qualidade dos cuidados pós-natais essenciais e de rotina prestados às mulheres e aos recém-nascidos, com o objetivo final de melhorar a saúde e o bem-estar materno e neonatal.
Uma “experiência pós-natal positiva” é um resultado importante para todas as mulheres que dão à luz e para os seus recém-nascidos, estabelecendo as bases para a melhoria da saúde e do bem-estar a curto e longo prazo. Uma experiência pós-natal positiva é definida como aquela em que as mulheres, pessoas que gestam, os recém-nascidos, os casais, os pais, os cuidadores e as famílias recebem informação consistente, garantia e apoio de profissionais de saúde motivados; e onde um sistema de saúde flexível e com recursos reconheça as necessidades das mulheres e dos bebês e respeite o seu contexto cultural.
Estas diretrizes consolidadas apresentam algumas recomendações novas e já bem fundamentadas sobre cuidados pós-natais de rotina para mulheres e neonatos que recebem cuidados no pós-parto em unidades de saúde ou na comunidade, independentemente dos recursos disponíveis.
É fornecido um conjunto abrangente de recomendações para cuidados durante o período puerperal, com ênfase nos cuidados essenciais que todas as mulheres e recém-nascidos devem receber, e com a devida atenção à qualidade dos cuidados; isto é, a entrega e a experiência do cuidado recebido. Estas diretrizes atualizam e ampliam as recomendações da OMS de 2014 sobre cuidados pós-natais da mãe e do recém-nascido e complementam as atuais diretrizes da OMS sobre a gestão de complicações pós-natais.
O estabelecimento da amamentação e o manejo das principais intercorrências é contemplada.
Recomendamos muito.
Vamos discutir essas recomendações no nosso curso de pós-graduação em Aleitamento no Instituto Ciclos.
Esta publicação só está disponível em inglês até o momento.
Prof. Marcus Renato de Carvalho
www.agostodourado.com
Phone Us ❤8107221448❤ #ℂall #gIRLS In Dehradun By Dehradun @ℂall @Girls Hotel...
Phone Us ❤8107221448❤ #ℂall #gIRLS In Dehradun By Dehradun @ℂall @Girls Hotel...chandankumarsmartiso
Phone Us ❤8107221448❤ #ℂall #gIRLS In Dehradun By Dehradun @ℂall @Girls Hotel With 100% Satisfaction
The Best Ayurvedic Antacid Tablets in India
Treat the symptoms of indigestion, heartburn and stomach reflux with the 10 Best Ayurvedic Antacid Tablets in India.
Recently uploaded (20)
Promoting Wellbeing - Applied Social Psychology - Psychology SuperNotes
Promoting Wellbeing - Applied Social Psychology - Psychology SuperNotes
Vestibulocochlear Nerve by Dr. Rabia Inam Gandapore.pptx
Vestibulocochlear Nerve by Dr. Rabia Inam Gandapore.pptx
Muscles of Mastication by Dr. Rabia Inam Gandapore.pptx
Muscles of Mastication by Dr. Rabia Inam Gandapore.pptx
share - Lions, tigers, AI and health misinformation, oh my!.pptx
share - Lions, tigers, AI and health misinformation, oh my!.pptx
Does Over-Masturbation Contribute to Chronic Prostatitis.pptx
Does Over-Masturbation Contribute to Chronic Prostatitis.pptx
Top 10 Best Ayurvedic Kidney Stone Syrups in India
Top 10 Best Ayurvedic Kidney Stone Syrups in India
Hemodialysis: Chapter 4, Dialysate Circuit - Dr.Gawad
Hemodialysis: Chapter 4, Dialysate Circuit - Dr.Gawad
Role of Mukta Pishti in the Management of Hyperthyroidism
Role of Mukta Pishti in the Management of Hyperthyroidism
8 Surprising Reasons To Meditate 40 Minutes A Day That Can Change Your Life.pptx
8 Surprising Reasons To Meditate 40 Minutes A Day That Can Change Your Life.pptx
Part II - Body Grief: Losing parts of ourselves and our identity before, duri...
Part II - Body Grief: Losing parts of ourselves and our identity before, duri...
Integrating Ayurveda into Parkinson’s Management: A Holistic Approach
Integrating Ayurveda into Parkinson’s Management: A Holistic Approach
Basavarajeeyam - Ayurvedic heritage book of Andhra pradesh
Basavarajeeyam - Ayurvedic heritage book of Andhra pradesh
Novas diretrizes da OMS para os cuidados perinatais de mais qualidade
Novas diretrizes da OMS para os cuidados perinatais de mais qualidade
Phone Us ❤8107221448❤ #ℂall #gIRLS In Dehradun By Dehradun @ℂall @Girls Hotel...
Phone Us ❤8107221448❤ #ℂall #gIRLS In Dehradun By Dehradun @ℂall @Girls Hotel...
Tests for analysis of different pharmaceutical.pptx
Tests for analysis of different pharmaceutical.pptx
March 19 Trig Review
- 2. Trigonometry is a set of tools that help determine the measures of a right triangle (sides and angles).
- 3. We are going to look at 3 of the Trig Tools: Sine, Cosine, and Tangent.
- 4. B hyp ote n use C A sine deals with an angles relationship with the opposite side and the hypotenuse. sinA = O/H sinB = O/H
- 5. B hyp ote n use C A Cosine deals with an angles relationship with the adjacent side and the hypotenuse. cosA = A/H cosB = A/H
- 6. B hyp ote n use C A Tangent deals with an angles relationship with the opposite side and the adjacent side. tanA = O/A tanB = O/A
- 7. B c 8 48° A C b A = 48° a=8 B=? b=? C=? c=?
- 8. B c 8 48° A C b
- 9. B 8 48° A C b
- 10. B 8 48° A C
- 11. B c 8 48° A C b A = 48° a=8 B=? b=? C=? c=?