Question

Find the exact value of each expression. Do not use a calculator.

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

Short answer

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

Step-by-step solution

Step 1. Given information.

The given expression is:

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

Step 2. Determine the exact value.

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

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

Step 3. Conclusion.

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