Answer
Using the reference angle $\theta'$, we can find the values of the trigonometric functions as follows:
$sin~\theta = -sin~\theta'$
$cos~\theta = -cos~\theta'$
$tan~\theta = tan~\theta'$
$csc~\theta = -csc~\theta'$
$sec~\theta = -sec~\theta'$
$cot~\theta = cot~\theta'$
Work Step by Step
Let $\theta$ be an angle in quadrant III. We can find a reference angle $\theta'$ in quadrant I.
$\theta' = \theta - 180^{\circ}$
In quadrant I, all the trigonometric functions have positive values. However, in quadrant III, only $tan~\theta$ and $cot~\theta$ have positive values, while $sin~\theta$, $cos~\theta$, $csc~\theta$, and $sec~\theta$ have negative values.
Using the reference angle $\theta'$, we can find the values of the trigonometric functions as follows:
$sin~\theta = -sin~\theta'$
$cos~\theta = -cos~\theta'$
$tan~\theta = tan~\theta'$
$csc~\theta = -csc~\theta'$
$sec~\theta = -sec~\theta'$
$cot~\theta = cot~\theta'$
