Question

PLEASE HELP!!!

Answer 1

Answer:

Step-by-step explanation:

First we'll simplify this using the Sum Identity for sin(x + y) where $x=\frac{3\pi}{2}$ and y = x. Notice we have 2 of those so we simplify first into

$2sin(\frac{3\pi}{2}+x)=-2$ and divide away the 2 on the left to get

$sin(\frac{3\pi}{2}+x)=-1$ and now we'll expand:

$sin\frac{3\pi}{2}cosx+cos\frac{3\pi}{2}sinx=-1$ and go to your unit circle to find the sin and cos of $\frac{3\pi}{2}$ and fill in where they go:

(-1cosx + 0sinx) = -1 which simplifies to

-1cosx = -1 so

cosx = 1 and

x = 0 or 2π, depending upon what your interval is.