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