Cos(π-θ) equals which of the following?

Question

A) cosθ

B) -cosθ

C) -sinθ

D) sinθ

Answer 1

use the sum and difference formula for cosines

cos(A-B) = cosAcosB - sinAsinB

cos(pi-x) = cospi(cosx) + sinpi(sinx) = (-1)cosx + 0 = -cosx

cos(pi-x) = -cosx

or use the fact that cosines are an even function

cosx = cos(-x)

then shift it by pi

cos(-x+pi) = -cos(-x) =-cosx