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

Stacey,

Use the double angle expression for cosine to write cos(2x) in terms of sin^{2}(x) and cos^{2}(x). Now use the fact that sin^{2}(x) + cos^{2}(x) = 1 to write cos2x as a function of sin^{2}(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

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