Question

How do you simplify `cos (pi - theta)`?

Answer 1

-cos t

Explanation:

Trig unit circle gives:
cos (pi - t) = -cos t

Answer 2

`cos(pi-theta)=-cos(theta)`

Explanation:

While a different answer mentions the unit circle, another way of arriving at the solution is to use the identity
`cos(alpha+beta) = cos(alpha)cos(beta)-sin(alpha)sin(beta)`
along with the fact that `cos(-alpha) = cos(alpha)`

With that, we have

`cos(pi-theta) = cos(pi+(-theta))`

`=cos(pi)cos(-theta)-sin(pi)sin(-theta)`

`=(-1)cos(-theta) - 0sin(-theta)`

`=-cos(-theta) - 0`

`=-cos(-theta)`

`=-cos(theta)`