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

Yes, the square bracket means the value is included in the interval, and ( or ) means excluded.
There are other notations where ( or ) is replaced by a square bracket pointing outwards, for example,
[0,2π) is the same as [0,2π[

To solve the above problem:
cos^2x=2+2sinx
Replace cos²x by (1-sin²x) and move everyting to one side to get:
sin²x+2sinx+1=0
Substitute p=sinx and solve the resulting quadratic equation for p.
Then solve for sin(x)=p for x∈ [0,2π).