Question

The terminal side of an angle in standard position passes through P(15,-8). What is the value of sin theta?

Answer 1

$\bf P(\stackrel{\stackrel{x}{adjacent}}{15},\stackrel{\stackrel{y}{opposite}}{-8})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{15^2+(-8)^2}\implies c=\sqrt{289}\implies c=17 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill sin(\theta )=\cfrac{\stackrel{opposite}{-8}}{\stackrel{hypotenuse}{17}}\hfill$