Prove the formula for the cosine of a sum, and build every other formula from it: sums, differences, double and triple angles, and the change of a sum into a product.
3 lessons, about 1 h 10 min3 simulations11 problems4 practice questionsPython in every lesson
Created by StemPy LabThe cosine of a sum is not the sum of the cosines. Two equal chords of the unit circle prove that . From this one formula come the formulae for , and , the allied angles, and exact values such as .
Put in the sum formulae: , has three forms, and . Turned round, the forms of give the half angles. One more step gives , and .
Adding and subtracting the sum formulae turns a product such as into a sum, and back. The sum-to-product formulae, such as , are the main tool for proving identities and for simplifying sums of sines and cosines.
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