Question

How do you simplify `cos (theta – 2pi)`?

Answer 1

`cos(theta)`

Explanation:

Use the cosine angle subtraction formula:

`cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)`

When applied to `cos(theta-2pi)`, we get

`cos(theta-2pi)=cos(theta)cos(2pi)+sin(theta)sin(2pi)`

Simplify, knowing that `cos(2pi)=1` and `sin(2pi)=0`.

`cos(theta-2pi)=cos(theta)xx1+sin(theta)xx0`

`cos(theta-2pi)=cos(theta)`

This should make sense. Since `2pi` is one revolution around the unit circle, the angles `theta` and `theta-2pi` are in the exact same locations, so `cos(theta)=cos(theta-2pi)`.