Answer
$\sin \theta = \frac{12}{13}$
$\cos \theta = -\frac{5}{13}$
$\tan \theta = -\frac{12}{5}$
$\csc \theta = \frac{13}{12}$
$\sec \theta = -\frac{13}{5}$
$\cot \theta = -\frac{5}{12}$
Work Step by Step
To find the trigonometric functions, we will first have to find $r$, that is the distance from the origin to the point $P(-5,12)$
Using Pythagorean Theorem :
$r=\sqrt{(-5)^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$
Now, using the general forms explained earlier in the chapter, we can write :
$\sin \theta = \frac{y}{r} = \frac{12}{13}$
$\cos \theta = \frac{x}{r} = -\frac{5}{13}$
$\tan \theta = \frac{y}{x} = -\frac{12}{5}$
$\csc \theta = \frac{r}{y} = \frac{13}{12}$
$\sec \theta = \frac{r}{x} = -\frac{13}{5}$
$\cot \theta = \frac{x}{y} = -\frac{5}{12}$
