solve for the equation x

Question

sin x= -.35
180<x<270

sin x= .2
90<x<180

cos x = -.72
180< x<270

please explain, thanks :)

Answer 1

Here is a standard way to solve these kind of problems, I will do the first one

sinx = -.35 , 180 < x <270

1. Find the acute angle, sometimes called the "angle in standard position"
by using the positive decimal
if sinx = .35, x = 20.5°

but x is supposed to be in III , then
x = 180 + 20.5 = 200.5°

check: on calculator, sin 200.5 = -.3502..

try the others the same way, check the answer with your calculator.