cos2x + sinx = 0 Find the exact solution of the equation with the interval (0, 2PI)?

Question

the intervals are 0 and 2 pie

Answer 1

cos 2x = 1 - 2(sin x)^2.
So we have 1 - 2(sin x)^2 + sin x = 0, or 2(sin x)^2 - sin x - 1 = 0.
That factorises as (2 sin x + 1)(sin x - 1) = 0.
So we have sin x = 1 or sin x = -0.5.

That gives x = pi/2 or x = 7pi/6 or x = 11pi/6.

Answer 2

Exact Solutions

Answer 3

erm is the cos2x supposed to be cos^2 x or just cos 2x?