Question

Find the values of $\cos^{-1}(\cos\frac{7\pi}{6})$ is equal to

• A. $\frac{7\pi}{6}$
• B. $\frac{5\pi}{6}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{6}$

Answer 1

Answer: (B)

$\frac{5\pi}{6}$

Answer 2

We know that $\cos^{-1}(cos \,x)=x$ if x∈[0,π] , which is the principal value branch of cos−1x.
Here,7π/6∉x∈[0,π].
Now,cos−1 (cos7π/6)can be written as:
cos−1 (cos7π/6)=cos−1 (cos-7π/6)=cos−1[(cos(2π-7π/6)] [cos(2π+x)=cosx]
=cos−1(cos5π/6) where 5π/6∈[0,π]
therefore cos−1(cos7π/6)=cos−1(cos5π/6)=5π/6.
The correct answer is B.