The value of cos^-1(cos 13π/6) is

Question

The value of  \(cos^{-1}\left(cos\frac{13\pi}{6}\right)\) is

A. \(\frac{13\pi}{6}\)

B. \(\frac{7\pi}{6}\)

C. \(\frac{5\pi}{6}\)

D. \(\frac{\pi}{6}\)

Answer 1

Correct Answer is \(\frac{\pi}{6}\)

Now, let x = \(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)

⇒ cos x =cos ( \(\frac{13\pi}{6}\)) 

Here ,range of principle value of cos is [0, π] 

⇒ x = \(\frac{13\pi}{6}\)∉ [0, π] 

Hence for all values of x in range [0, π] ,the value of 

\(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)is 

⇒ cos x =cos (2π - \(\frac{\pi}{6}\)) (\(\because\) cos ( \(\frac{13\pi}{6}\))= cos (2π - \(\frac{\pi}{6}\)) ) 

⇒ cos x =cos ( \(\frac{\pi}{6}\)) ( \(\because\)cos (2π - θ)= cosθ) 

⇒ x = \(\frac{\pi}{6}\)