Show that cos(pi - θ) = -cos θ

Question

for every angle θ

Answer 1

Using the unit circle on an x-y graph, draw terminal arms with angles θ and pi-θ
These will be in quadrants I and II, let their endpoints be (x,y) and (-x,y).

from their endpoints drop lines to the x-axi, giving you two right-angles triangles that are similar.

from the first triangle:
cos θ = x/1 = x

from the second triangle:
cos(pi-θ ) = -x/1
x = -cos(pi-θ)

equating the two x's

-cos(pi-θ) = cos θ or
cos(pi-θ) = -cos θ