Question

How do I graph these parametric equations on the interval (pi/2 , 3pi/2)x(θ) = 3 cos θy(θ) = 6 sin θ

Answer 1

Given:

`x(\theta)=3cos\theta\text{ and }y(\theta)=6sin\theta.`

Required:

We have to draw the graphs of the given function.

Step-by-step explanation:

To draw the graph of the given functions proceeds as follows:

We know how to draw the graphs of sine and cosine functions. The given functions are multiples of sine and cosine.

`x((\pi)/(2))=3cos((\pi)/(2))=3*0=0`
`x(\pi)=3cos(\pi)=3*-1=-3`
`x((3\pi)/(2))=3cos((3\pi)/(2))=3*0=0`

Hence the graph of the function is

Similarly,

`y((\pi)/(2))=6sin((\pi)/(2))=6*1=6`
`y(\pi)=6sin(\pi)=6*0=0`
`y((3\pi)/(2))=6sin((3\pi)/(2))=6*-1=-6.`

Hence the graph of the function is

Final answer:

Hence the final answer is the two graph above. That is

And