Chapter 5.3, Problem 6CFU

To determine

To find: The value of $\sec \left(-{90}^{\circ }\right)$ using the unit circle.

Answer to Problem 6CFU

  $\sec \left(-{90}^{\circ }\right)\text{}\text{is undefined}$

Explanation of Solution

Given information: $\sec \left(-{90}^{\circ }\right)$

Calculation:

  

A unit circle. The secant of − 90 located straight down (- 90 is coterminal with +270).

  $\sec =\frac{1}{\cos }$ According to the circle diagram,

  $\cos {270}^{\circ }=0$

So,

  $\sec -{90}^{\circ }=\frac{1}{0}$

That is undefined.

  

You can see on the graph that at 270 degrees,

  $\left(\frac{3\pi }{2}\right)=1.4\times 3.14=4.71$

You notice as asymptote at 4.71, this means the graph (secant) is undefined here as expected.