Math CentralQuandaries & Queries


Question from Katelyn, a student:

Hi Math Central,

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? sin2(x) + cos2(x) = 1 so sin2(x) = 1 - cos2(x).

Thus you get 1 - cos2(x) =cos(x), which is a quadratic you can solve like any other (let y = cos x, then you just solve 1 - y2 = y; then use arccosine to find x).

Stephen La Rocque.

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