Find the value of sin^{- 1} (sin 2π/3)

Solution:

Inverse trigonometric functions as a topic of learning are closely related to the basic trigonometric ratios.

The domain (θ  value)  and the range(answer) of the trigonometric ratio are changed to the range and domain of the inverse trigonometric function.

Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios. 

Here the basic trigonometric function of Sin θ = y can be changed to θ = sin^-1 y

Since,

sin θ = sin (π - θ)

Therefore,

sin^{- 1} (sin 2π / 3)

= sin^{- 1} [sin (π - 2π/3)]

= sin^{- 1} (sin π / 3)

= π / 3

Hence,

sin^{- 1} (sin 2π / 3) = π / 3

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.2 Question 16

Find the value of sin^{- 1} (sin 2π/3)

Summary:

The value of sin^{- 1} (sin 2π/3) is π / 3. Inverse trigonometric functions as a topic of learning are closely related to the basic trigonometric ratios