I have been having some real trouble in trying to solve this equation:

sin^2(x) = -2cosx

I know I can use the squared identity for sine and change the problem into:

(1-cos2x)/2 = -2cosx

Although I don't know what to do once I have done this step if indeed it is the right one.
I hope you can help!

- Katelyn

Hi Katelyn.

Why not use the pythagorean identity instead? sin^{2}(x) + cos^{2}(x) = 1 so sin^{2}(x) = 1 - cos^{2}(x).

Thus you get 1 - cos^{2}(x) =cos(x), which is a quadratic you can solve like any other (let y = cos x, then you just solve 1 - y^{2} = y; then use arccosine to find x).

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.