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Q. 46

Expert-verified
Found in: Page 381

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the exact value of each expression. Do not use a calculator.$\mathrm{sec}\pi -\mathrm{csc}\frac{\pi }{2}$

The exact value of the given expression is $-2$.

See the step by step solution

## Step 1. Given information.

The given expression is:

$\mathrm{sec}\pi -\mathrm{csc}\frac{\pi }{2}$

## Step 2. Determine the exact value.

In the trigonometric table $\mathrm{sec}\pi =-1$ and $\mathrm{csc}\frac{\pi }{2}=1$. Substitute these values in the given expression.

$\begin{array}{rcl}\mathrm{sec}\pi -\mathrm{csc}\frac{\pi }{2}& =& \left(-1\right)-\left(1\right)\\ & =& -2\end{array}$

## Step 3. Conclusion.

The exact value of the given expression is $-2$.