Question

Solve for x given the interval of [0,2pi).

cos^2x=2+2sinx

I got (3pi)/2 or 270 degrees..

By the way, does the notation [0,2pi) mean
0<=x<2 pi or 360?

Answer 1

The reason they usually use [0,2pi) is that 0 and 2pi are really the same angle. So, your solution set need not include them both.

cos^2x-2sinx-2 = 0
1-sin^2x-2sinx-2 = 0
sin^2x+2sinx+1 = 0
sinx = -1
so, yes x = 3pi/2