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Product to Sum Calculator

Convert products of sines and cosines to sums using product-to-sum formulas.

Calculator

Product Type

Unit

DegreesRadians

Angle A

Angle B

All Product-to-Sum Formulas

sin A · cos B = ½[sin(A+B) + sin(A-B)]

cos A · sin B = ½[sin(A+B) - sin(A-B)]

cos A · cos B = ½[cos(A-B) + cos(A+B)]

sin A · sin B = ½[cos(A-B) - cos(A+B)]

Memory tip: Products of same functions (sin·sin or cos·cos) give cosines. Products of different functions (sin·cos) give sines.

Frequently Asked Questions

When are product-to-sum formulas useful?

For integrating products of trig functions, solving certain trig equations, and in signal processing and Fourier analysis.

What's prosthaphaeresis?

A historical technique for multiplication using trig tables and these formulas. Before calculators, it was faster to look up values and add than to multiply large numbers!

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