Sum-to-Product & Product-to-Sum Calculator
Apply the sum-to-product and product-to-sum identities.
Enter Two Angles
In degrees
Results
Enter two angles and click calculate.
Why these identities matter
Sum-to-product and product-to-sum identities convert between sums and products of sines/cosines. They show up everywhere from integration in calculus to signal processing and Fourier analysis.
Frequently Asked Questions
What is the sum-to-product identity?▾
sin A + sin B = 2 sin((A+B)/2) cos((A−B)/2), and similar formulas for cos A ± cos B and sin A − sin B.
What is the product-to-sum identity?▾
sin A cos B = ½[sin(A+B) + sin(A−B)], with parallel formulas for cos·cos, sin·sin, and cos·sin.
Where are these used?▾
In calculus (integration), in physics (wave interference and beat frequencies), and in signal processing.
Are they hard to memorize?▾
A bit. Most people remember the structure (half-sum and half-difference of A and B) and look up the exact form when needed.