Question

x=2 cos (t), y=3sin (t), 0 ≤ t ≤ 2π A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

Answer 1

To sketch the curve represented by the given parametric equations, plug in different values of t, calculate the corresponding x and y values, and plot them on a graph.

Step-by-step explanation:

The given parametric equations are:

x = 2 cos(t)

y = 3 sin(t)

To sketch the curve represented by the parametric equations, we can plug in different values of t, calculate the corresponding values of x and y, and plot them on a graph. Since the range of t is from 0 to 2π, we can choose various values of t (e.g., 0, π/2, π, 3π/2, 2π) and find the corresponding x and y values to plot the points. Connecting these points will give us the sketch of the curve.