2. Suppose the position (x, y) of a particle at time t is given by the parametric equations [x(t) = sin (t), (y(t) = cos² (t), - 2π ≤ t ≤ 2πT. (a) Eliminate the parameter t to find a Cartesian equation for the path traced by the particle. (b) Draw a graph to depict the motion of the particle for −2 ≤ t ≤ 2. On your graph, mark the start and end points and the direction of motion of the particle.
2. Suppose the position (x, y) of a particle at time t is given by the parametric equations [x(t) = sin (t), (y(t) = cos² (t), - 2π ≤ t ≤ 2πT. (a) Eliminate the parameter t to find a Cartesian equation for the path traced by the particle. (b) Draw a graph to depict the motion of the particle for −2 ≤ t ≤ 2. On your graph, mark the start and end points and the direction of motion of the particle.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Suppose the position (x, y) of a particle at time t is given by the parametric equations
[x(t) = sin(t),
y(t) = cos² (t),
- 2π ≤ t ≤ 2π.
(a) Eliminate the parameter t to find a Cartesian equation for the path traced by the particle.
(b) Draw a graph to depict the motion of the particle for -2 ≤ t ≤ 2. On your graph, mark
the start and end points and the direction of motion of the particle.
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