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

Trigonometric Functions Class 11
Trigonometric Functions Class 11
Trigonometric Functions Class 11
Trigonometric Functions Class 11
Trigonometric Functions Class 11
Trigonometric Functions Class 11
Trigonometric Functions Class 11


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