Question

Find cos(−2205°) and sin(−2205°). Identify the measure of the reference angle.

Answer 1

Reference angle is 45°

`sin(-2205^(\circ))=-0.707`

`cos(-2205^(\circ))=0.707`

Explanation:

We have given as
`cos(-2205^(\circ))`

Which can be written as
`cos(-2205^(\circ))=cos(-12\pi -45^(\circ))`

Here angle is
`-45^(\circ)` which is equal to 315°

We know that 315° lies in forth quadrant

And in forth quadrant reference angle is given by
`360-angle`

So reference angle will be
`360-315=45^(\circ)`

Now
`cos(-2205^(\circ))=cos(-12\pi -45^(\circ))=cos(45)=0.707`

`sin(-2205^(\circ))=sin(-12\pi -45^(\circ))=-sin(45)=-0.707`