Question

Evaluate sin(Tan^-10)

Answer 1

$\tan x=0$ for $x=n\pi$, where $n$ is any integer. The inverse tangent function returns numbers between $-\dfrac\pi2$ and $\dfrac\pi2$. The only multiple of $\pi$ in this range is 0, so $\tan^{-1}0=0$.

Then

$\sin\left(\tan^{-1}0\right)=\sin0=\boxed0$