Answer
$\frac{5\sqrt {34}}{34}, \frac{3\sqrt {34}}{34}, \frac{5}{3}, \frac{3}{5}, \frac{\sqrt {34}}{3}, \frac{\sqrt {34}}{5}$
Work Step by Step
1. Graph $5x-3y=0, x\geq0$ and the least positive angle $\theta$ as shown. We can identify a point $(3,5)$ on the line.
2. $sin\theta=\frac{5}{\sqrt {(3)^2+(5)^2}}=\frac{5}{\sqrt {34}}=\frac{5\sqrt {34}}{34}$
3. $cos\theta=\frac{3}{\sqrt {(3)^2+(5)^2}}=\frac{3}{\sqrt {34}}=\frac{3\sqrt {34}}{34}$
4. $tan\theta=\frac{5}{3}$
5. $cot\theta=\frac{1}{tan\theta}=\frac{3}{5}$
6. $sec\theta=\frac{1}{cos\theta}=\frac{\sqrt {34}}{3}$
7. $csc\theta=\frac{1}{sin\theta}=\frac{\sqrt {34}}{5}$
