Q 34. - Precalculus Enhanced with Graphing Utilities

Question

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

$\cos 180°-\sin 180°$

Step-by-Step Solution

Answer

The exact value of$\cos 180°+\sin 180°=-1$

Step 1. Given information

$\cos 180°-\sin 180°$

Step 2. Solution

$$\begin{gathered} \cos 180°=\cos (180°-0°)=-\cos 0°=-1 \\ \sin 180°=\sin (180°+0°)=-\sin 0°=0 \\ \mathrm{Putting} \mathrm{the} \mathrm{values} \mathrm{in} \mathrm{the} \mathrm{given} \mathrm{expression} \mathrm{we} \mathrm{get}, \\ -1-0=-1 \\ \mathrm{So}, \\ \cos 180°+\sin 180°=-1 \end{gathered}$$