# What is the exact value of cos(-5pi/4)??

May 29, 2018

$- \frac{\sqrt{2}}{2}$

#### Explanation:

You need your Unit Circle for this one. First, convert the negative radian into a positive one by adding $2 \pi$ ( $\frac{8 \pi}{4}$ with the common denominator) so you get $\frac{3 \pi}{4}$. Then, find that radian on the Unit Circle and its x-value since you're looking for cosine. Because it's in Quadrant II the x-value is negative and there you have it.

May 29, 2018

$\textcolor{b l u e}{\cos \left(5 \frac{\pi}{4}\right) = - \frac{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{2}}{\sqrt{2}}\right) = - \frac{\sqrt{2}}{2}}$

#### Explanation:

Note that:

$\textcolor{red}{\cos \left(- x\right) = \cos \left(x\right)}$

$\cos \left(- 5 \frac{\pi}{4}\right) = \cos \left(5 \frac{\pi}{4}\right)$

$5 \frac{\pi}{4} = 225$

$\cos \left(5 \frac{\pi}{4}\right)$ lies in the third quadrant.

$\cos x$ is only positive in the first and the forth quadrant.

$\cos \left(5 \frac{\pi}{4}\right) = - \frac{1}{\sqrt{2}} \cdot \left(\frac{\sqrt{2}}{\sqrt{2}}\right) = - \frac{\sqrt{2}}{2}$