solve the following trig equation :

Question

7 = 8sin(1/2)x. I can solve this using the half-angle indentity. But i need to solve this using period and phase change equation. how do i do this?

Answer 1

7 = 8sin(1/2)x

sin (1/2)x = .875

so (1/2)x is in the first or second quadrant, and
(1/2)x = 61.04º or (1/2)x = 118.96º

then x = 237.9º or 122.1º

but the period of your curve is 720º

so by adding/subtractin 720º to/from any of the found angles will give you more answers.

in general
x = 122.1 + 720k or
x = 237.9 + 720k , where k is an integer.