3sin2x-2cosx=0 the interval is 0 degrees<x<360 degrees?

Answer 1

You can use the double angle formula to rewrite the sin term:

3sin(2x) - 2cos(x) = 0
3[2sin(x)cos(x)] - 2cos(x) = 0
3sin(x)cos(x) - cos(x) = 0
cos(x)[3sin(x) - 1] = 0

cos(x) = 0
x = 90, 270

3sin(x) - 1 = 0
3sin(x) = 1
sin(x) = 1/3
x = 19.47