Mathematics: Find cos(1680°) and sin(1680°). identify the measure of the reference angle.

Find cos(1680°) and sin(1680°). identify the measure

A1A2T3

07.01.2022

Reference angle will be $60^{\circ}$

$cos(1680)=\frac{-1}{2}$

sin(1680)=-0.866

Step-by-step 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 $cos(1640)=cos(9\pi +60)=-cos60=\frac{-1}{2}$

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

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