Q 22. - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value. Do not use a calculator.

$\cos \left(7\mathrm{\pi }\right)$

Step-by-Step Solution

Answer

The exact value of$\cos \left(7\mathrm{\pi }\right)=-1$

Step 1. Given information

$\cos \left(7\mathrm{\pi }\right)$

Step 2. Unit circle

$$\begin{gathered} \mathrm{Rotate} \mathrm{anticlockwise} \mathrm{to} \mathrm{form} 7\mathrm{\pi } \mathrm{angle} \mathrm{with} \mathrm{the} \mathrm{positive} \mathrm{x}-\mathrm{axis}. \\ \mathrm{The} \cos \left(7\mathrm{\pi }\right) \mathrm{equals} \mathrm{the} \mathrm{x}-\mathrm{coordinate}(-1) \mathrm{of} \mathrm{the} \mathrm{point} \mathrm{of} \mathrm{intersection} (-1, 0) \mathrm{of} \mathrm{unit} \mathrm{circle}. \end{gathered}$$

Step 3. Final answer

$\cos \left(7\mathrm{\pi }\right)=\mathrm{x}=-1$