Of course you can do this algebraically using the cosine difference formula, but let's think about it from a geometric point of view. The number 180° - θ is diametrically opposite to the number θ. With this, we can show that these two points lie on the same diameter with end points 180° - θ and θ on the unit circle. Knowing this, we can easily conclude then that
sin(180° - θ ) = - sin θ
cos(180° - θ) = - cos θ,
using the fact that 180° - θ and θ are just opposite each other on the same diameter.