# Question #32016

Aug 15, 2015

Refer below

#### Explanation:

$\cos \left(\frac{3 \pi}{2} + x\right)$
$= \cos \left(- \frac{\pi}{2} + x\right)$ (because $\cos x = \cos \left(x + 2 \pi\right)$)
$= \cos \left(\frac{\pi}{2} - x\right)$ (because $\cos \left(- x\right) = \cos x$)
$= \sin x$
$= 0.3$

Aug 15, 2015

The answer is $\cos \left(\frac{3 \pi}{2} + x\right) = 0.3$. Here is a different path than Joel Kindiak's to the same answer.

#### Explanation:

Use the cosine of a sum formula:

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

$= \left(- 1\right) \cos \left(x\right) - \left(- 1\right) \left(0.3\right)$

$= 0.3$