# If Cos(theta)= 2/3 then what is cos(theta + pi)?

Oct 4, 2016

$\cos \left(\theta + \pi\right) = - \frac{2}{3}$

#### Explanation:

Use the formula cos(A+B)=cosAcosB-sinAsinB.So
$\cos \left(\theta + \pi\right) = \cos \theta \cos \pi - \sin \theta \sin \pi$

$= \frac{2}{3} \left(- 1\right) - \sin \theta \left(0\right)$

Note that we can find the sin of theta from the given ratio but since sine of pi is 0 we don't have to bother finding it.

$= - \frac{2}{3} - 0$

$= - \frac{2}{3}$