Question

For an angle Θ with the point (12, -5) on its terminating side, what is the value of cosine?

Answer 1

by definition of polar coordinates, we can write:
\[\left\{ \begin{gathered}
12 = r\cos \theta \hfill \\
- 5 = r\sin \theta \hfill \\
\end{gathered} \right.\]

Answer 2

squaring both formulas above, and summing them each other, we get:
\[144 + 25 = {r^2}\]
So what is r?

Answer 3

r is 13

Answer 4

that's right!