Question from Jamie, a student:

Hi. I'm am having trouble with a problem on my math homework. I need help rewriting the expression in terms of cosine to the first degree. (sinx)^4(cosx)^2

Hi Jamie.

The multiple angle formulas help. First I know that

sin(2t) = 2 sin(t) cos(t)

so

sin^{4}(x) cos^{2}(x) = = sin^{2}(x) [sin(x)cos(x)]^{2} = ^{1}/_{4} sin^{2}(x) sin^{2}(2x)

Now use the fact that

cos(2t) = cos^{2}(t) - sin^{2}(t) = 1 - 2 sin^{2}(t)

I hope this helps, Harley