CPM Homework Help : PC Problem 4-87

Given $\text{cot }β =\frac { \sqrt { 7 } } { 3 }$ and $β$ is in Quadrant III ( $\pi< β <\frac { 3 \pi } { 2 }$ ), find the following values. Try drawing a triangle where $\text{cot }β =\frac { \sqrt { 7 } } { 3 }$ and find the missing side. Next determine if the value you are finding is positive or negative based on the location of the angle.

$\text{cos }β$
Step 1(a):
What must the signs be for
the coordinates in Quadrant III?
Step 2(a):
$\text{cot}\beta=\frac{\text{cos}\beta}{\text{sin}\beta}=\frac{-\sqrt{7}}{-3}$
Step 3(a):
Find the missing side. Note: The hypotenuse is always $+$ .
Find the $\text{cos }β$ .

$\text{csc }β$
Hint (b):
Follow a similar thinking process as in (a).