Question

`cos^-1 (cos  (4pi)/3)` = ______.

Options

• \[\frac{5\pi}{6}\]

• \[\frac{\pi}{3}\]

• \[\frac{4\pi}{3}\]

• \[\frac{2\pi}{3}\]

Answer 1

`cos^-1 (cos  (4pi)/3)` = \[\underline{\frac{2\pi}{3}}\]

Explanation:

`cos^-1 (cos  (4pi)/3)`

`= cos^-1 {cos (pi + pi/3)}`

`= cos^-1 (- cos  pi/3)`

`= pi - cos^-1 (cos  pi/3)`  ....[∵ cos^-1 (- x) = π - cos^-1 x]

`= pi - pi/3 = (2pi)/3`