Answer
See below:
Work Step by Step
Equation (1) is of the form $ y=A\sin \left( Bx-C \right)$.
We can undertake the following steps to determine the graph of the equation:
Step 1. Here, $ A=-4$ and $ B=\pi $ such that
$\begin{align}
& \text{Amplitude}=\left| -4 \right| \\
& =4
\end{align}$
$\begin{align}
& \text{Period}=\frac{2\pi }{B} \\
& =\frac{2\pi }{\pi } \\
& =2
\end{align}$
$\begin{align}
& \text{Quarter period}=\frac{2}{4} \\
& =\frac{1}{2}
\end{align}$
Step 2. Now we will find the $ x $ -values by adding the quarter periods.
The cycle starts at $ x=0$, such that
$\begin{align}
& x=0 \\
& x=0+\frac{1}{2}=\frac{1}{2} \\
& x=\frac{1}{2}+\frac{1}{2}=1 \\
& x=1+\frac{1}{4}=\frac{3}{2}
\end{align}$
Step 3. Now, we will evaluate the function at each value of $ x $.
At $ x=0$,
$\begin{align}
& y=-4\cos \left( \pi x \right) \\
& =-4\cos \left( {{0}^{\circ }} \right) \\
& =-4
\end{align}$
Therefore, the coordinates are $\left( 0,-4 \right)$.
At $ x=\frac{1}{2}$,
$\begin{align}
& y=-4\cos \left( \pi \cdot \frac{1}{2} \right) \\
& =-4\cos \left( \frac{\pi }{2} \right) \\
& =0
\end{align}$
Therefore, the coordinates are $\left( \frac{1}{2},0 \right)$.
At $ x=1$,
$\begin{align}
& y=-4\cos \left( \pi \cdot 1 \right) \\
& =-4\cos \left( \pi \right) \\
& =4
\end{align}$
Therefore, the coordinates are $\left( 1,4 \right)$.
At $ x=\frac{3}{2}$,
$\begin{align}
& y=-4\cos \left( \pi \cdot \frac{3}{2} \right) \\
& =-4\cos \left( \frac{3\pi }{2} \right) \\
& =0
\end{align}$
Therefore, the coordinates are $\left( \frac{3}{2},0 \right)$.
Step 4. On connecting these points, the graph can be obtained.