Q 40. - Precalculus Enhanced with Graphing Utilities

Question

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

$5 \cos 90° -8 \sin 270°$

Step-by-Step Solution

Answer

The exact value of$5 \cos 90°-8 \sin 270°=8$

Step 1. Given information

$5 \cos 90° -8 \sin 270°$

Step 2. Calculation

$$\begin{gathered} \cos 90°=0 \\ \sin 270°=\sin (180°+90°)=-\sin 90°=-1 \\ \tan 270°=-1 \\ \mathrm{Putting} \mathrm{the} \mathrm{values} \mathrm{in} \mathrm{the} \mathrm{given} \mathrm{expression} \mathrm{we} \mathrm{get}, \\ (5\times 0)-(8\times -1)=8 \\ \mathrm{So}, \\ 5 \cos 90°-8 \sin 270°=8 \end{gathered}$$