Q 32. - Precalculus Enhanced with Graphing Utilities

Question

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

$\sin 30°-\cos 45°$

Step-by-Step Solution

Answer

The exact value of$\sin 30°-\cos 45°=\frac{1-\sqrt{2}}{2}$

Step 1. Given information

$\sin 30°-\cos 45°$

Step 2. Solution

$$\begin{gathered} \sin 45°=\frac{1}{2} \\ \cos 45°=\frac{1}{\sqrt{2}} \\ \mathrm{Putting} \mathrm{the} \mathrm{values} \mathrm{in} \mathrm{the} \mathrm{given} \mathrm{expression} \mathrm{we} \mathrm{get}, \\ \frac{1}{2}-\frac{1}{\sqrt{2}}=\frac{\sqrt{2}-2}{2\sqrt{2}}=\frac{\sqrt{2}(1-\sqrt{2})}{2\sqrt{2}}=\frac{1-\sqrt{2}}{2} \\ \mathrm{So}, \\ \sin 30°-\cos 45°=\frac{1-\sqrt{2}}{2} \end{gathered}$$