Chapter 5.3, Problem 16E

To determine

To find: The value of $\cot \left(-{180}^{\circ }\right)$ using the unit circle.

Answer to Problem 16E

  $\cot \left(-{180}^{\circ }\right)\text{ is undefined}$

Explanation of Solution

Given information: $\cot \left(-{180}^{\circ }\right)$

Calculation:

  

Here is the unit circle in degrees.

We want,

  $\cot \left(-{180}^{\circ }\right)=\frac{1}{\tan -{180}^{\circ }}$

Since $\tan =\frac{\sin }{\cos }\text{ and }-{180}^{\circ }$ is coterminal, with $+{180}^{\circ }$ , then

  $\tan =\frac{0}{-1}=0$

But the cotangent is the reciprocal of this so it is $\frac{1}{0}$ ,

That is undefined.