# maths formulas for class 10 trigonometry

Trigonometry is a very important chapter for board exams. It has good weightage in the exam,3-4 questions are always asked in all board exams. Here are all formulas for class 10 trigonometry, which you have to prepare for the board exam.

## Trigonometric ratios formula for class 10 and its PDF

In class 10th, we study trigonometry only in the right angled-triangle. Three sides of the right-angled triangle are known as hypotenuse, base, and perpendicular.Here are formulas for class 10 trigonometry

Hypontuse: The longest side of the triangle and opposite to the right angle is called the hypotenuse.

Base: It is the bottom side of any right-angled triangle.

perpendicular: It is the height of the right-angled triangle.

θ=It is the angle between hypotenuse and base

Here are six trigonometric ratios for a right-angled triangle

Sinθ=\frac{perpendicular}{Hypontuse}

Cosθ=\frac{Base}{Hypontuse}

Tanθ=\frac{Perpendicular}{base}

Secθ=\frac{Hyponetuse}{Base}

Cosecθ=\frac{Hyponetuse}{perpendicular}

Cotθ=\frac{Base}{perpendicular}

These ratios are also related to each other as follows

Sinθ=\frac{1}{cosecθ}

Cosθ=\frac{1}{secθ}

Tanθ=\frac{1}{cotθ}

Tanθ=\frac{sinθ}{cosθ}

Cotθ=\frac{cosθ}{sinθ}

Here is a trigonometric table for class 1o at an angle from 0º to 90º

## Trigonometric ratios of complementary angles

Complementary angle: When the sum of two angles of a triangle is 90º, then it is called complementary angles of each other.

Example: Let A and B are two angles whose sum is 90º.Then,

∠A is called the complement of ∠B

∠B  is called the complement of ∠A

This relation is not only in angles but also in trigonometric ratios as follows

Sin(90-θ)=Cosθ

Cos(90-θ)=Sinθ

Tan(90-θ)=Cotθ

Cot(90-θ)=Tanθ

Sec(90-θ)=Cosecθ

Cosec(90-θ)=Secθ

## Trigonometric identities class 10 formula

These three trigonometric identities are very important. Because we use it to proving all other trigonometric identities in trigonometry for class 10

(1) sin²θ+cos²θ=1

cos²θ=1-sin²θ

sin²θ=1- cos²θ

This is true when 0º≤ A ≤ 90º

(2) 1+tan²θ=sec²θ

tan²θ=sec²θ-1

sec²θ-tan²θ=1                             {This identity is used to prove good level probelm,so always remember it}

This is true when 0º≤ A ≤ 90º

(3) 1+cot²θ=Cosec²θ

cot²θ=Cosec²θ-1

Cosec²θ-cot²θ=1                       {This identity is used to prove good level probelm,so always remember it}

But, this is true when 0º<A ≤ 90º. Because CosecA and secA are not defined when A=0º