Answer
We can see a sketch of the least positive angle $\theta$ below.
We can find the trigonometric values:
$sin ~\theta = \frac{y}{r} = \frac{-3}{5}$
$cos ~\theta = \frac{x}{r} = \frac{-4}{5}$
$tan ~\theta = \frac{y}{x} = \frac{3}{4}$
$csc ~\theta = \frac{r}{y} = \frac{5}{-3}$
$sec ~\theta = \frac{r}{x} = \frac{5}{-4}$
$cot ~\theta = \frac{x}{y} = \frac{4}{3}$
Work Step by Step
$3x-4y=0$
$\frac{y}{x} = \frac{3}{4} = \frac{-3}{-4}$
Since $x \leq 0$, we can let $x=-4$ and $y=-3$
Then $r = \sqrt{(-4)^2+(-3)^2} = 5$
We can see a sketch of the least positive angle $\theta$ below.
We can find the trigonometric values:
$sin ~\theta = \frac{y}{r} = \frac{-3}{5}$
$cos ~\theta = \frac{x}{r} = \frac{-4}{5}$
$tan ~\theta = \frac{y}{x} = \frac{3}{4}$
$csc ~\theta = \frac{r}{y} = \frac{5}{-3}$
$sec ~\theta = \frac{r}{x} = \frac{5}{-4}$
$cot ~\theta = \frac{x}{y} = \frac{4}{3}$
