Question

the point (5, -2) is on the terminal ray of angle θ, which is in standard position. without evaluating, explain how you would find the values of the six trigonometric functions.

Explanation:

For a point $(x,y)=(5, - 2)$ on the terminal - ray of an angle $\theta$ in standard position, first find the distance $r$ from the origin $(0,0)$ to the point $(x,y)$ using the formula $r=\sqrt{x^{2}+y^{2}}$. Then, the six trigonometric functions are defined as follows: $\sin\theta=\frac{y}{r}$, $\cos\theta=\frac{x}{r}$, $\tan\theta=\frac{y}{x}(x
eq0)$, $\csc\theta=\frac{r}{y}(y
eq0)$, $\sec\theta=\frac{r}{x}(x
eq0)$, $\cot\theta=\frac{x}{y}(y
eq0)$.

Answer:

First find $r = \sqrt{x^{2}+y^{2}}$ with $x = 5$ and $y=-2$. Then use $\sin\theta=\frac{y}{r}$, $\cos\theta=\frac{x}{r}$, $\tan\theta=\frac{y}{x}$, $\csc\theta=\frac{r}{y}$, $\sec\theta=\frac{r}{x}$, $\cot\theta=\frac{x}{y}$ (with appropriate non - zero conditions).