Answer
$-\frac{12}{13}, \frac{5}{13}, -\frac{12}{5}, -\frac{5}{12}, \frac{13}{5}, -\frac{13}{12}$
Work Step by Step
1. Graph $12x+5y=0, x\geq0$ and the least positive angle $\theta$ as shown. We can identify a point $(5,-12)$ on the line.
2. $sin\theta=\frac{-12}{\sqrt {(5)^2+(-12)^2}}=-\frac{12}{13}$
3. $cos\theta=\frac{5}{\sqrt {(5)^2+(-12)^2}}=\frac{5}{13}$
4. $tan\theta=\frac{-12}{5}=-\frac{12}{5}$
5. $cot\theta=\frac{1}{tan\theta}=-\frac{5}{12}$
6. $sec\theta=\frac{1}{cos\theta}=\frac{13}{5}$
7. $csc\theta=\frac{1}{sin\theta}=-\frac{13}{12}$
