Suppose we are given

θ = sin –1 x

Empty triangle - Inverse Trigonometry.jpg

We need to find sin θ , cos θ and tan θ

Now,

  θ = sin –1 x

So,

  sin θ = x

  sin θ = x/1

 

And we know that

  sin θ =  (Side opposite to angle θ)/Hypotenuse

  x/1 = AB/AC 

So, AB = x, AC = 1

 

Now, in right triangle Δ ABC

By Pythagoras Theorem

  AC 2 = AB 2 + BC 2

  1 2 = x 2 + BC 2

  1 – x 2 = BC 2

  BC = √(1-x 2 )

Filled triangle - Inverse Trigonometry.jpg

Value of sin and cos when sin inverse is given.jpg

Value of sin θ , cos θ , tan θ when θ is given as inverse

Value of sin, cos, tan when angle is given as inverse.jpg

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.