Question

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

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

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 given Parametric Equation $x\left(t\right)=4\sin t+2\sin \left(2t\right),y\left(t\right)=4\cos t+2\cos \left(2t\right)$

$$\begin{gathered} X_{1T}=4\sin t+2\sin \left(2t\right) \\ {Y}_{1T}=4\cos t+2\cos \left(2t\right) \end{gathered}$$

Step 2. Select a viewing Window.

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

Select the graph button