Trigonometric ratios
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In this presentation the main focus is on understanding the relationships between three sides and three angles of a triangle using some basic ratios called trigonometric ratios. We also discussed Pythagoras theorem to determine the value of hypotenuse or base or perpendicular in a right angled triangle using its standard formulae. We discussed about how to determine the perpendicular and base with respective to a specific angle in right angled triangle. We can apply these trigonometric ratios and Pythagoras theorem concepts in solving questions of class 10th NCERT, RBSE or any other board books. ................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .......................VIDEO LECTURE OF THIS PRESENTATION.................................. .................................... https://youtu.be/iPaiMb1OvN0 ......................................... .............................. https://mathsolutionpoint.blogspot.com/p/10-th.html ...................
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Trigonometric ratios relate the sides of a right triangle to an angle of the triangle. There are three basic ratios: sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. These ratios can be remembered using the mnemonic "SOH-CAH-TOA". Trigonometric ratios will be the same for any similar triangles, as the ratios of corresponding sides will be equivalent.
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.
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.
Trigonometry
This is a school standard presentation for class 10 students .
It will be very helpful to you all.
Hope you all like this .
And pass your exams with flying colors
Trigonometry
Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.
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.
Shivam goyal ix e
The document discusses various properties of quadrilaterals:
- It defines the six types of quadrilaterals - trapezium, parallelogram, rectangle, rhombus, square, and kite.
- It provides examples and definitions for each type.
- Several theorems regarding the properties of parallelograms are presented, including that the diagonals of a parallelogram bisect each other and that opposite sides of a parallelogram are equal.
- Additional theorems state that a quadrilateral is a parallelogram if opposite sides are equal or if opposite angles are equal.
Quadrilaterals
1) A quadrilateral is a geometric figure with four sides, four angles, and two diagonals. The sum of the angles is always 360 degrees.
2) There are six types of quadrilaterals: trapezoid, parallelogram, rectangle, rhombus, square, and kite. A parallelogram has both pairs of opposite sides parallel. A rectangle has one right angle. A square is both a rectangle and rhombus with all sides equal.
3) Theorems include: the diagonals of a parallelogram bisect each other; if the diagonals of a quadrilateral bisect each other it is a parallelogram; a quadrilateral is
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.
quadrilateral
This document discusses properties of quadrilaterals. It begins with definitions of different types of quadrilaterals based on the number of pairs of parallel sides they have: trapezoids have 1 pair, parallelograms have 2 pairs. It then discusses properties of parallelograms and special types of parallelograms like rectangles, rhombi, and squares. Several theorems about the properties of parallelograms are then proved, such as opposite sides being equal, opposite angles being equal, and diagonals bisecting each other.
Trigonometric functions
A very comprehensive lesson on TRIGONOMETRIC Function.
Helpful for A-level & Hssc mathematics level students.
Properties of a triangle
This document discusses various properties of triangles, including:
- Triangles have three sides, three vertices, and three angles.
- Triangles can be classified based on sides (scalene, isosceles, equilateral) and angles (acute, obtuse, right).
- Key properties include: a triangle's three medians intersect at the centroid; a triangle has three altitudes drawn from each vertex to the opposite side; the measure of a triangle's three angles sum to 180 degrees.
Mathematics-Inroduction to Trignometry Class 10 | Smart eTeach
Mathematics-Inroduction to Trignometry Class 10 | Smart eTeachSmart eTeach IGS Infotec Global Pvt Ltd
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The document defines different types of triangles based on their sides and angles. It discusses triangles formed by three non-collinear points connected by line segments. The types of triangles include scalene, isosceles, equilateral, acute, right, and obtuse triangles. Congruence rules for triangles are provided, including SAS, ASA, AAS, SSS, and RHS. Properties of triangles like angles opposite equal sides being equal and sides opposite equal angles being equal are explained. Inequalities relating sides and angles of triangles are described.
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Mathematics-Inroduction to Trignometry Class 10 | Smart eTeach
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- 1. Trigonometric Ratios & Pythagoras Theorem Fundamental Concepts Class-X (NCERT, RBSE)
- 2. Trigonometry Ratios Consider a right triangle ABC as shown in adjacent figure : 1. There are three angles in this triangle as follows : A. AngleABC = 90 degree B. Angle BAC = Acute Angle (less than 90 degree) C. Angle BCA = Acute Angle(less than 90 degree) A CB Perpendicular Base
- 3. Trigonometry Ratios If we consider angle BAC then : 1. Side opposite to this angle is called perpendicular i.e. BC is perpendicular. 2. Side AC is called hypotenuse. And 3. Side AB is called Base. C AB Perpendicular Base A CB Perpendicular Base Consider a right triangle ABC as shown in adjacent figure : If we consider angle BCA then : 1. Side opposite to this angle is called perpendicular i.e. is AB perpendicular. 2. Side AC is called hypotenuse. And 3. Side BC is called Base.
- 4. Trigonometry Ratios The trigonometry ratios with respect to angle BAC or angle A are as follows: Ratio Formula Triangle ABC sin A Perpendicular/Hypotenuse BC/AC cosec A Hypotenuse/Perpendicular AC/BC cos A Base/Hypotenuse AB/AC sec A Hypotenuse/Base AC/AB tan A Perpendicular/Base BC/AB cot A Base/Perpendicular AB/BC C AB Perpendicular Base
- 5. Trigonometry Ratios The trigonometry ratios with respect to angle BCA or angle C are as follows: Ratio Formula Triangle ABC sin C Perpendicular/Hypotenuse AB/AC cosec C Hypotenuse/Perpendicular AC/AB cos C Base/Hypotenuse BC/AC sec C Hypotenuse/Base AC/BC tan C Perpendicular/Base AB/BC cot C Base/Perpendicular BC/AB A CB Perpendicular Base
- 6. Trigonometry Ratios Additional ratios With respect to angle A or angle BAC sin A = 1/cosec A cosec A= 1 / sin A cos A = 1 / sec A sec A = 1 / cos A tan A = 1 / cot A cot A = 1 / tan A Additional ratios With respect to angle C or angle BCA sin C = 1/cosec C cosec C= 1 / sin C cos C = 1 / sec C sec C = 1 / cos C tan C = 1 / cot C cot C = 1 / tan C
- 7. Pythagoras Theorem (Hypotenuse)2 = (Perpendicular)2+(Base)2 (Perpendicular)2 = (Hypotenuse)2 - (Base)2 (Base)2 = (Hypotenuse)2 - (Perpendicular)2 A CB Perpendicular Base Pythagoras Theorem