Q 31. - 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$\sin 45°+\cos 45°=\sqrt{2}$

Step 1. Given information

$\sin 45°+\cos 45°$

Step 2. Solution

As we can see from the table above, 

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