Chapter 9.4, Problem 59E

To determine

To match:

The parametric equation $x=2\cos \theta ,y=\sin 2\theta$ with the correct graph from the following options:

  

Answer to Problem 59E

Correct option (b). The graph shown by option (b) is correctly matches with parametric equation $x=2\cos \theta ,y=\sin 2\theta$ .

  

Explanation of Solution

Given information:

  

Calculation:

Know that:

The parametric equations of Lissajous curve are $x=2\cos \theta ,y=\sin 2\theta$

Since, $-1\le \cos \theta \le 1$ therefore $-2\le x\le 2$

Since, $-1\le \sin 2\theta \le 1$ therefore $-1\le x\le 1$

So,

The domain is defined as: $\left[-2,2\right]$

The range is defined as: $\left[-1,2\right]$

Therefore the domain and range shown by the graph (b) is correct for the given parametric equations of Lissajous curve: