Q. 22 - Precalculus Enhanced with Graphing Utilities

Question

In problems 11-26, use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\csc \left(\frac{9\pi }{2}\right)$

Step-by-Step Solution

Answer

The exact value is $1.$

Step 1. Given information.

We have:

$\csc \left(\frac{9\pi }{2}\right)$

Step 2. Find the exact value of trigonometric function.

The function is $\csc \left(\frac{9\pi }{2}\right)$.

Formula used:

$\csc \left(\mathrm{\theta }+2\mathrm{\pi }\right)=\csc \left(\mathrm{\theta }\right)$

Here, $\theta =\frac{\pi }{2}$

$$\begin{gathered} \csc \left(\frac{9\pi }{2}\right)=\frac{1}{\sin \left(\frac{9\pi }{2}\right)} \\ =\frac{1}{\sin \left(\frac{\pi }{2}\right)} \\ =\frac{1}{1} \\ =1 \end{gathered}$$