Question

In Problems 45 – 48, use a graphing utility to graph the curve defined by the given parametric equations.

$x=4\sin t-2\sin \left(2t\right),y=4\cos t-2\cos \left(2t\right)$

Short answer

The graph is shown in the figure.

Step-by-step solution

Step 1. Given Information

The given parametric equations are

$$\begin{gathered} x=4\sin t-2\sin \left(2t\right), \\ y=4\cos t-2\cos \left(2t\right) \end{gathered}$$

Step 2. Drawing a Graph

Step 1. Enter the equation $$\begin{gathered} x=4\sin t-2\sin \left(2t\right), \\ y=4\cos t-2\cos \left(2t\right) \end{gathered}$$with the graphic utility in the PARametric mode.

Step 2. Select the viewing window. The interval $\left[0,2\mathrm{\pi }\right]$, so we select the following square viewing window:

$$\begin{gathered} T_{min}=0,T_{max}=2\mathrm{\pi },T_{step}=0.1 \\ {X}_{min}=-8,X_{max}=8,X_{scl}=1 \\ {Y}_{min}=-8,Y_{max}=8,Y_{scl}=1 \end{gathered}$$

Step 3. Finally select Graph