Q 35. - Precalculus Enhanced with Graphing Utilities

Question

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

$\sin 45° \cos 45°$

Step-by-Step Solution

Answer

The exact value of$\sin 45° \cos 45°=\frac{1}{2}$

Step 1. Given information

$\sin 45° \cos 45°$

Step 2. Solution

$$\begin{gathered} \sin 45°=\frac{1}{\sqrt{2}} \\ \cos 45°=\frac{1}{\sqrt{2}} \\ \mathrm{Putting} \mathrm{the} \mathrm{values} \mathrm{in} \mathrm{the} \mathrm{given} \mathrm{expression} \mathrm{we} \mathrm{get}, \\ \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=\frac{1}{2} \\ \mathrm{So}, \\ \sin 45° \cos 45°=\frac{1}{2} \end{gathered}$$