Math: why sin(180° – x) = sinx

Tutoring math, trig identities are important. The tutor mentions one.

An identity, meaning something always true, is

sin(a – b) = sin(a)cos(b) – cos(a)sin(b)

Therefore,

sin(180° – x) = sin(180°)cos(x) – cos(180°)sin(x)

Since sin(180°) = 0 and cos(180°) = -1 (which one can confirm on their calculator), we have

sin(180° – x) = 0*cosx – (-1)sinx

And so

sin(180° -x) = sinx

Source:

Travers, Kenneth et al. Using Advanced Algebra. Toronto: Doubleday Canada Limited, 1977.