Question

Find the exact value of the expression please!
sin(tan^-1 2)

Answer 1

\(\bf tan^{-1}(2)\implies tan^{-1}\left(\cfrac{2}{1}\right)\implies \cfrac{\textit{opposite side}}{\textit{adjacent side}}\implies \cfrac{b}{a}\\ \quad \\
\textit{pythagorean theorem }c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\\ \quad \\
sin(\theta)=\cfrac{b}{c}\implies \cfrac{\textit{opposite side}}{\textit{hypotenuse}}\)