# How do you do simplify cos [sec ^-1 (-5)]?

Nov 6, 2015

$- \frac{1}{5}$

#### Explanation:

$\cos \left[{\sec}^{-} 1 \left(- 5\right)\right]$

Finding the value of the Composition:

Lets being to solve the equation by working on the inside. Immediately we can see that ${\sec}^{-} 1 \left(\frac{5}{- 1}\right)$ isn't a special angle. If you noticed how I attached the negative sign to "1" is because sec = $\frac{r}{x}$. The radius can not be negative. and "1" serves as the x-value in this equation.

Note: The inverse of cosine (secant) is restricted between $0 < x < \pi$. (This would matter if it were asking for sin instead of cos because the y-value would become negative and give you a wrong answer).

Now cosine is $\frac{x}{r}$. So simply put the values where they belong.

$\cos \left(\frac{- 1}{5}\right)$ = $- \frac{1}{5}$

This is not a special angle so leave the answer as a improper fraction or decimal. Whatever your instructor prefers. :)