Find $\sin\left(300\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)\right)$

Question

Did it as follows: $\sin\left(300\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)\right)=\sin\left(300\left(\pi-\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)\right)\right)$. I don't know how to proceed to the next step, as 300 stands here.

Answer 1

arccos(-sqrt(2)/2) = 3π/4

300arccos(-sqrt(2)/2) =225π

on the unit circle 225π corresponds to π

so sin(225π)=sin(π)=0

Answer 2

We know that $\displaystyle \arccos\left(-\frac{\sqrt2}{2}\right)=\frac{3π}{4}$

If we multiply that by $300$, we get $225π$.

We know that $\sin(225π)=\boxed{0}$

Answer 3

We start with:

$\arccos\left(-\frac{\sqrt2}{2}\right)=\frac{3π}{4}$.

Then you multiply 300 by $\frac{3π}{4}$, and you get:

$225π$.

Next, convert you answer to degrees and you'll get 40500. Divide that by 360° and you get 112.5 which means there's 112 full circles, and then a half. Half a circle is 180°, thus $225π$ = $\sin(225π)$ = $\sin(π)$ = $\boxed{0}$.