# Trigonometric Functions Class 11

Trigonometric Functions Class 11 – If radius r is the radius of circle and an arc of length l units subtends an angle $\theta$ radians, then $l=r\theta$. 1 Radian = $\frac{\pi }{180}$ degree and 1 Degree = $\frac{180 }{\pi}$ radian. Trigonometric Equations are equations involving trigonometric functions of a variable. Principal solution of a trigonometric equation is a solution for which $0 \leq x < 2π$. The expression involving integer ‘n’ that gives all solutions of a trigonometric equation is called the general solution.

Some trigonometric Identities:

1. $cos^{2}x+sin^{2}x=1$
2. $sec^{2}x-tan^{2}x=1$
3. $cosec^{2}x-cot^{2}x=1$
4. $cos(2n\pi +x)=cos x$
5. $sin(2n\pi +x)=sin x$
6. $cos(-x)=cos x$
7. $sin(-x)=-sin x$
8. $cos(x+y)=cos\;x\;\;cos\;y\;-\;sin\;x\;\;sin\;y$
9. $cos(x-y)=cos\;x\;\;cos\;y\;+\;sin\;x\;\;sin\;y$
10. $sin(x+y)=sin\;x\;\;cos\;y\;+\;cos\;x\;\;sin\;y$
11. $sin(x-y)=sin\;x\;\;cos\;y\;-\;cos\;x\;\;sin\;y$
12. $cos\;2x=cos^{2}x-sin^{2}x=2cos^{2}x-1=1-2sin^{2}x=\frac{1-tan^{2}x}{1-tan^{2}x}$
13. $sin\;2x=2cosx\;.\;sinx=\frac{2tanx}{1+tan^{2}x}$

### Trigonometric Functions Class 11 Examples

#### Practise This Question

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1=a2=...=a10=150 and a10,a11,... are in an AP with common difference - 2, then the time taken by him to count all notes is