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Old 04-30-2001, 01:03 PM
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)?
Old 04-30-2001, 01:54 PM
Join Date: May 2000
Location: Massachusetts
Posts: 41,543

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:


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.
“Of course,” said my grandfather, stepping from the Time Machine and pulling a gun from his belt, “There’s no paradox if I shoot you!”

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