Answer
(a) $\frac{4}{5}$
(b) $\frac{\sqrt 3}{3}$
Work Step by Step
(a) Let $u=arctan\frac{4}{3}$, we have $tan(u)=\frac{4}{3}$. Form a right triangle of sides $4,3,5$ and angle $u$ facing the side $4$, we have $sin(u)=\frac{4}{5}\longrightarrow u=arcsin\frac{4}{5}\longrightarrow arcsin(x)=arcsin\frac{4}{5}$, thus $x=\frac{4}{5}$
(b) Since $arcsin\frac{\sqrt 3}{2}=\frac{\pi}{3}$, we have $arccot(x)+\frac{2\pi}{3}=\pi \longrightarrow arccot(x)=\frac{\pi}{3}$, thus $x=cot(\frac{\pi}{3})=\frac{\sqrt 3}{3}$
