Question

PLEASE HELP!!!

Solve for x in the following equation!!!


`sin((3\pi )/(2)+x) + sin((3\pi )/(2)+x)=-2`

Answer 1

Explanation:

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

`2sin((3\pi)/(2)+x)=-2` and divide away the 2 on the left to get

`sin((3\pi)/(2)+x)=-1` and now we'll expand:

`sin(3\pi)/(2)cosx+cos(3\pi)/(2)sinx=-1` and go to your unit circle to find the sin and cos of
`(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.