Question #48588

1 Answer
Douglas K.
Nov 19, 2016

The product is zero when either factor is zero. Please see the explanation.

Explanation:

Treat it like a factored quadratic; the product is zero when either factor is zero:

sin(alpha) = 0 and cos(beta) = 0sin(α)=0andcos(β)=0

The sine function is zero at, n, multiples of piπ and the cosine function is zero at pi/2π2 plus n multiples of piπ, where n is any negative or positive integer, including zero.

alpha = npi and beta = pi/2 + npi; n = ..., -3, -2, -1, 0, 1, 2, 3,...

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