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| Math Central | Quandaries & Queries |
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Question from stacey, a student: solve the equation cos2x = sinx for 0 < x < 2 pi |
Stacey,
Use the double angle expression for cosine to write cos(2x) in terms of sin2(x) and cos2(x). Now use the fact that sin2(x) + cos2(x) = 1 to write cos2x as a function of sin2(x). This allows you to write cos2x = sinx as a quadratic equation in sin(x). Factor this quadratic and solve for sin(x).
I hope this helps,
Harley
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