Question

How do you find the exact value for `cos 240`?

Answer 1

it equals `(-1/2)` because `cos(60^@) = 1/2`

Explanation:

The reference angle for `240^@` is `60^@` (since `240^@ = 180^@ + 60^@`)

`60^@` is an angle of one of the standard triangles with
`cos(60^@) = 1/2`

`240^@` is in the 3rd quadrant so (either by CAST or noting that the "x-side" of the associate triangle is negative)
`cos(240^@) = -cos(60^@)`

`cos(240^@) = -1/2`