Question

three trigonometric functions for a given angle are shown below.
\\(\csc\alpha=\frac{13}{12},\sec\alpha =-\frac{13}{5},\cot\alpha=-\frac{5}{12}\\)
what are the coordinates of point \\((x,y)\\) on the terminal ray of angle \\(\alpha\\), assuming that the values above were not simplified?
\\( (-5,12)\\)
\\( (5,-12)\\)
\\( (-12,5)\\)
\\( (12,-5)\\)

Explanation:

Step1: Recall trigonometric - function definitions

We know that $\csc\alpha=\frac{r}{y}=\frac{13}{12}$, so $r = 13$ and $y=12$. Also, $\sec\alpha=\frac{r}{x}=-\frac{13}{5}$, so $x=- 5$.

Step2: Determine the point coordinates

The coordinates of a point $(x,y)$ on the terminal - ray of an angle $\alpha$ in standard position are given by $(x,y)$. Since $x = - 5$ and $y = 12$, the point is $(-5,12)$.

Answer:

A. $(-5,12)$