Question

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

$$\begin{gathered} x=\sin t+\cos t, \\ y=\sin t-\cos t \end{gathered}$$

Short answer

The graph is shown in the figure.

Step-by-step solution

Step 1. Given Information

The given parametric equations are

$$\begin{gathered} x=\sin t+\cos t, \\ y=\sin t-\cos t \end{gathered}$$

Step 2. Drawing Graph

Step 1. Enter the equation $x\left(t\right)=\sin t+\cos t,y\left(t\right)=\sin t-\cos t$with the graphic utility in the PARametric mode.

Step 2. Select the viewing window. The interval $t>0$, so we select the following square viewing window:

$$\begin{gathered} T_{min}=0,T_{max}=2\mathrm{\pi },T_{step}=0.1 \\ {X}_{min}=-6,X_{max}=6,X_{scl}=1 \\ {Y}_{min}=-6,Y_{max}=6,Y_{scl}=1 \end{gathered}$$

Step 3. Finally select Graph