# How do you evaluate arcsec (sec(-pi/3))?

Apr 19, 2015

$\frac{\pi}{3}$

First $\sec \left(- \frac{\pi}{3}\right)$ would be equal to $\sec \left(\frac{\pi}{3}\right)$ = 2. ( Angle -$\frac{\pi}{3}$ lies in the fourth quadrant and because cosine is positive there sec would also be positive).

Now the problem is reduced to evaluating arcsec2. Since $\sec \left(\frac{\pi}{3}\right)$ is 2, hence arcsec2 would be equal to $\frac{\pi}{3}$

Apr 19, 2015

$\theta = a r c \sec \left(\sec \left(- \frac{\pi}{3}\right)\right)$

$\sec \theta = \sec \left(- \frac{\pi}{3}\right)$

$\therefore \theta = - \frac{\pi}{3}$