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#1
04-30-2001, 12:03 PM
 WarmNPrickly Guest Join Date: Oct 1999 Posts: 5,441
I know that sin^2(theta) = 1 - cos 2Xtheta. Is there a similar formula relating sin^3(theta) to sin(3Xtheta) or cos(3Xtheta)?
#2
04-30-2001, 12:54 PM
 CalMeacham Member Join Date: May 2000 Location: Massachusetts Posts: 42,033
Christopher:

You left off a factor of 1/2 in your formula for sin^2. Your right hand side gives twice the value of sin^2.

The formulas you're looking for are:

sin^3(A)=(3/4)sin(A)-(1/4)sin(3A)

cos^3(A)=(3/4) cos(A)+(1/4)cos(3A)

You can find these formulas in Fundamental Formulas of Physics Donald Menzel, ed. Dover Books section 2.5. It's also in Table of Integral, Series, and Products ed. I.S. Gradshteyn and I.M. Ryzhik, Academic Press, section 1.31.

Or you can write the mutiple angle out in complex form and extract the real and imaginary parts.
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