Question

cot(sin^-1 x/3)

Answer 1

Arcsine of x/3 represents some angle.\[\Large\rm \sin^{-1}\left(\frac{x}{3}\right)=\theta\]We want to rewrite this in terms of sine, not inverse sine,\[\Large\rm \sin \theta=\frac{x}{3}\]

Answer 2

Recall that:\[\Large\rm \sin \theta=\frac{opposite}{hypotenuse}\]We can show this relationship by drawing a right triangle.