Chapter 5.3, Problem 1CFU

To determine

To explain: $\csc {180}^{\circ }$ is undefined.

Explanation of Solution

Given information: $\csc {180}^{\circ }$

Calculation:

  

  $\csc {180}^{\circ }\text{is what}$ we are looking at.

Since $\csc$ is $\frac{1}{\sin }$ let’s look at sin.

We know that for any fraction, 0 is not allowed as a denominator.

So we can’t have $\sin =0$ but sine is a cyclic function and if you look at a sine graph given $\sin \theta =0$ for all multiples of $\pi \left({180}^{\circ }\right)\text{ so}\frac{1}{\sin }$ is undefined.

Since this is cosecant by definition, the $\csc \text{ of }\theta$ is also undefined for any multiple of ${180}^{\circ }$