Question

For an angle 0 with the point (-20,-21) on its terminating side, what is the value of cosine ?

Answer 1

check the picture below.

$\bf (\stackrel{a}{-20},\stackrel{b}{-21})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-20}\\ b=\stackrel{opposite}{-21}\\ \end{cases} \\\\\\ c=\sqrt{(-20)^2+(-21)^2}\implies c=\sqrt{841}\implies c=29 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-20}}{\stackrel{hypotenuse}{29}}~\hfill$