verify sin degrees

Question

verify sin(180 degrees-θ)=sin θ sine difference identity to rewrite right side of equation got some of this wrong she said

Answer 1

The difference identity for Sine is:

Then...

Answer 2

The angle difference identity for sine is:

So:

sin(180° - θ) = sin(180°)cos(θ) - cos(180°)sin(θ)

From the Unit Circle:

sin(180°) = 0

cos(180°) = -1

So the equation simplifies to:

sin(180° - θ) = 0*cos(θ) - (-1)*sin(θ)

sin(180° - θ) = 0 + 1*sin(θ)

sin(180° - θ) = sin(θ)