Question

IMPORTANT [how do you]Find sin theta if tan theta = 3/4

Answer 1

$\bf tan(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{adjacent}{4}}\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{3^2+4^2}\implies c=5 \\\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{hypotenuse}{5}}$

bear in mind that, though the square has two valid roots, one negative and one positive, the hypotenuse is just a radius distance, and therefore is never negative.