Answer
See graph and explanations.
Work Step by Step
1. Graph the line $3x-4y=0, x\leq0$ (red) as shown, with angle $\theta$ also shown in the figure.
2. We can find a point on the line as $(-4,-3)$
3. We have $sin\theta=\frac{-3}{\sqrt {(-4)^2+(-3)^2}}=-\frac{3}{5}$
4. We have $cos\theta=-\frac{4}{5}$
5. We have $tan\theta=\frac{3}{4}$
6. We have $cot\theta=\frac{4}{3}$
7. We have $sec\theta=\frac{1}{cos\theta}=-\frac{5}{4}$
8. We have $csc\theta=\frac{1}{sin\theta}=-\frac{5}{3}$
