Chapter 10, Problem 1RE

To determine

Whether the statement “A point on the graph of $y=2\cos x$ is $\left(\pi ,-2\right)$” is true or false.

Answer to Problem 1RE

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

The given function is, $y=2\cos x$ and the point is $\left(\pi ,-2\right)$.

Substitute $x=\pi \text{ and }y=-2$ in $y=2\cos x$.

$\begin{array}{l}y=2\cos x\\ -2=2\cos \left(\pi \right)\\ -2=-2\left(1\right)\\ -2=-2\text{ True}\end{array}$

Thus, the point $\left(\pi ,-2\right)$ is on the graph of $y=2\cos x$.

Therefore, the given statement is $\underset{\_}{\text{true}}$.