Math CentralQuandaries & Queries


Question from stacey, a student:

solve the equation cos2x = sinx for 0 < x < 2 pi
giving the answer in terms of pi.


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,

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