Question

The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.

Answer 1

$\bf P(\stackrel{a}{8}~,~\stackrel{b}{6})\impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{8^2+6^2}\implies c=\sqrt{64+36}\implies c=\sqrt{100}\implies c=10 \\\\\\ sin(\theta)=\cfrac{\stackrel{b}{opposite}}{\stackrel{c}{hypotenuse}}\implies sin(\theta )=\cfrac{6}{10}\implies sin(\theta )=\cfrac{3}{5}$