Question

Question #48588

Answer 1

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) = 0`

The sine function is zero at, n, multiples of `pi` and the cosine function is zero at `pi/2` plus n multiples of `pi`, 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,...`