Q. 42 - Precalculus Enhanced with Graphing Utilities

Question

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

$2\sin \frac{\pi }{4}+3\tan \frac{\pi }{4}$

Step-by-Step Solution

Answer

The exact value of the given expression is $\sqrt{2}+3$.

Step 1. Given information.

The given expression is:

$2\sin \frac{\pi }{4}+3\tan \frac{\pi }{4}$

Step 2. Determine the exact value.

In the trigonometric table $\sin \frac{\pi }{4}=\frac{1}{\sqrt{2}}$ and $\tan \frac{\pi }{4}=1$. Substitute these values in the given expression.

$\begin{array}{rcl}2\sin \frac{\pi }{4}+3\tan \frac{\pi }{4}& =& 2\left(\frac{1}{\sqrt{2}}\right)+3\left(1\right)\\ & =& \sqrt{2}+3\end{array}$

Step 3. Conclusion.

The exact value of the given expression is $\sqrt{2}+3$.