Question

Find cos(1680°) and sin(1680°). Identify the measure of the reference angle.

Answer 1

Reference angle will be
`60^(\circ)`

`cos(1680)=(-1)/(2)`

`sin(1680)=-0.866`

Explanation:

We have given
`cos(1680^(\circ))`

It can be written as
`cos(1680^(\circ))=cos(8\pi +240)`

As 240° is lie in the third quadrant

And we know that for third quadrant

Reference angle is given by
`angle-180^(\circ)`

So reference angle will be
`240^(\circ)-180^(\circ)=60^(\circ)`

Now
`cos(1640)=cos(9\pi +60)=-cos60=(-1)/(2)`

`sin(1640)=cos(9\pi +60)=-sin60=-0.866`