Plot the parametric equations???

Question

Plot the parametric equations below.

 

x=6 cos t

y=4 sin t

Answer 1

Let's re-write the equations, and use a trig identity to get an idea of the plot.

 

First, solve each equation for the trig function:

x/6 = cos t

y/4 = sin t

 

Now, we use the following trig identity: 

cos² t + sin² t = 1

 

Make substitutions for sin t and cos t from the first set of equations:

(x/6)² + (y/4)² = 1

 

This is the equation of an ellipse, centered at the origin, with a horizontal major axis.

 

Vertices: (±6,0)

Co-vertices: (0,±4)

 

Plot these points, and connect them with a smooth oval.

Answer 2

topeqn  has an amplitude of 6, starts at six at t=0, goes down thru zero to -6 and back up thru 0 to 6 and repeats.

 

bottom eqn has an amplitude of 4, starts at 0 at t=0 and goes up to 4, down thru 0 to -4 and back up thru 4 to 4 and repeats.

 

Both plots complete one cycle in 2Pi radians or 360 degrees and both also repeat in both positive and negative t directions.