solving the following equation for x in the interval?

Question

hi

i would like to find out how to solve
the following equation for x in the interval
zero is less than or equal to x is less than or equal to 2 pi
4 cos( 2 x ) +sin( x ) = 4 (this is the equation)
to 2 decimal places
thanks for your help

Answer 1

4 cos 2x + sin x = 4
4( 1 - 2 sin² x ) + sin x = 4
4 - 8 sin² x + sin x = 4
8 sin² x - sin x = 0
sin x ( 8 sin x - 1 ) = 0

so:

sin x = 0
or
sin x = 1/8

Even you should be able to solve x from that..

Answer 2

get x by itself