# Thread: How do I calculate this cosine?

1. ## How do I calculate this cosine?

How do I calculate $cos 7\pi/8$
I only know how to find it if it is on the unit circle >_>

2. Originally Posted by dorkymichelle
How do I calculate $cos 7\pi/8$
I only know how to find it if it is on the unit circle >_>
first, note that $\cos\left(\frac{7\pi}{8}\right) < 0$

let $x = \frac{7\pi}{4}$

use the half-angle formula ...

$\cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1+\cos{x}}{2}}$

3. Why do you use [tex] x = 7\pi/4?
and the half formula? I don't see the "half" part

4. Hello dorkymichelle
Originally Posted by dorkymichelle
Why do you use [tex] x = 7\pi/4?
and the half formula? I don't see the "half" part
$\cos x=\cos\left(\frac{7\pi}{4}\right)=\cos\left(2\pi -\frac{\pi}{4}\right) =\frac{1}{\sqrt2}$

$\frac{1}{2} \cdot \frac{7\pi}{4}$ = ?