Question

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

$\cos 180°-\sin 180°$

Short answer

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

Step-by-step solution

Step 1. Given information

$\cos 180°-\sin 180°$

Step 2. Solution

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