# Question #26248

Jan 28, 2018

$- 0.9$

#### Explanation:

Rotating an angle by $\pi$ flips it 180 degrees around the circle.

This means that both its $x$ and $y$ coordinates are flipped (made negative).

Since $\cos$ is just the $x$ coordinate of an angle on the unit circle, and rotating that angle by $\pi$ will flip its $x$ coordinate (and its $y$ too, but that's not important right now) we can say that:

$\cos \left(\theta + \pi\right) = - \cos \theta$

Therefore:

$\mathmr{if} \cos \theta = 0.9$

$\text{then} \cos \left(\theta + \pi\right) = - 0.9$