Here is my problem:
$$ \sin(\cos^{-1} \frac{2}{5} ) $$
I know how to do it for the most part; I just draw a triangle with sides 2,5 and √21 and I then find the sine (opposite/hypotenuse) of the angle whose cosine is 2/5. The answer is √21/5. But is there a simpler way to tackle this problem that doesn`t involve as much work? Any feedback would be much appreciated!
Nope. In general we take $y = \cos^{-1}{\left(\frac{2}{5}\right)}$ or $\cos y = \frac{2}{5}$ so $\sin y = \frac{\sqrt{21}}{5}$