# What is cos [Sec ^-1 (-5)]?

Oct 17, 2015

#cos(arcsec(-5)) = -1/5

#### Explanation:

Knowing that $\cos \left(x\right) = \frac{1}{\sec} \left(x\right)$ we can say that

$\cos \left(a r c \sec \left(- 5\right)\right) = \frac{1}{\sec} \left(a r c \sec \left(- 5\right)\right)$

Since $\sec \left(a r c \sec \left(x\right)\right) = x$ we have

$\cos \left(a r c \sec \left(- 5\right)\right) = \frac{1}{- 5} = - \frac{1}{5}$