Question

Find the exact value of sec()θfor the angle in standard position passing through the point (-3, 2) on its terminal side.

Answer 1

Well, we know the angle θ terminal location, is at -3,2, so the adjacent side is -3 and the opposite side is 2, so it looks like the picture below, therefore

$\bf (\stackrel{a}{-3}~,~\stackrel{b}{2})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+2^2}\implies c=\sqrt{13}\qquad \qquad \qquad sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\stackrel{adjacent}{-3}}$