### Home > PC > Chapter 4 > Lesson 4.2.2 > Problem4-87

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.

1. $\text{cos }β$

What must the signs be for
$\text{cot}\beta=\frac{\text{cos}\beta}{\text{sin}\beta}=\frac{-\sqrt{7}}{-3}$
Find the missing side. Note: The hypotenuse is always $+$.
Find the $\text{cos }β$.
1. $\text{csc }β$