Answer
See graph:
$sin\theta=\frac{3\sqrt {34}}{34} $
$cos\theta=\frac{5\sqrt {34}}{34} $
$tan\theta=\frac{3}{5} $
$csc\theta=\frac{\sqrt {34}}{3} $
$sec\theta=\frac{\sqrt {34}}{5} $
Work Step by Step
Given $cot\theta=\frac{5}{3} $, we can draw a right triangle as shown in the figure.
The hypotenuse $x$ can be found as $x=\sqrt {5^+3^2}=\sqrt {34}$ and the other
five trigonometric ratios are:
$sin\theta=\frac{3}{\sqrt {34}}=\frac{3\sqrt {34}}{34} $
$cos\theta=\frac{5}{\sqrt {34}}=\frac{5\sqrt {34}}{34} $
$tan\theta=\frac{3}{5} $
$csc\theta=\frac{\sqrt {34}}{3} $
$sec\theta=\frac{\sqrt {34}}{5} $
