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| Math Central | Quandaries & Queries |
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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. - 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).
Cheers,
Stephen La Rocque.
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