Find the principal value of cos^-1 (- 1/2)

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

Let,

cos^-1 (- 1/2)

cos y = - 1 / 2

= - cos (π / 3)

= cos (π - π / 3)

= cos (2π / 3)

Range of the principal value of cos^{- 1} (x)

= [0, π]

Thus,

principal value of cos^-1 (- 1/2)

= (2π / 3)

---

NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 5

Find the principal value of cos^-1 (- 1/2)

Summary:

The principal value of cos^-1 (- 1/2)  = (2π / 3).  Range of the principal value of cos^{- 1} (x)  = [0, π]