Question

Identify the parametric equations that represent the same path as the following parametric equations.

x(t)=2cos2t
y(t)=sin3t

a. x(t)=2cos2t
y(t)=sin6t
b. x(t)=4cos4t
y(t)=sin6t
c. x(t)=2cos4t
y(t)=sin6t
d. x(t)=4cos2t
y(t)=2sin3t

Answer 1

Finding Parametric Equations Quiz

1. Which set of parametric equations represents the following function? y=√x+3
A. x(t) = 5t
y(t) = √5t+3

2. Identify the parametric equations that represent the same path as the following parametric equations. Select all that apply. x(t)=t y(t)=3t²-4
A. x(t) = 2t
y(t) = 12t² - 4
B. x(t) = -t
y(t) = 3t² - 4

3. (Your question)
C. x(t) = 2cos4t
y(t) = sin6t

Answer 2

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Generally this parameter is given by t. This type of equations are commonly used to express the coordinates of the points that make up a geometric object like a curve or surface, in which case the equations are collectively called a parametric representation or parameterization. In the figures below, the equation:

`\left \{ {{x(t)=2cos2t} \atop {y(t)=sin3t}} \right.`

matches with this one:

`\left \{ {{x(t)=2cos4t} \atop {y(t)=sin6t}} \right.`