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

Solution:

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

Let,

sin^{- 1} (- 1/2) = y

Hence,

sin y can be written as (- 1/2)

= - sin (π / 6)

= sin (- π / 6)

Range of the principal value of sin^-1 (x) is

(- π / 2, π / 2)

Thus, principal value of sin^{- 1} (- 1/2)

= (- π / 6)

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 1

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

Summary:

The principal value of sin^{- 1} (- 1/2) = (- π / 6)