W6Q2P1 We would like to understand how a parametric equation represents a curve and distinguish some small differences among similar parametric equations:For the following parametric equations, use a table (shown below)tXyof values of t, x and y to find several points of the curve and then sketch the curve:i) x == -t², y = t + 6, -4≤t≤4ii) x = −t+7, y=-5t-5,iii) x = 3 cos 2t, y = 3 sin 2t,-5 ≤t≤50≤t≤ π

Answered: We would like to understand how a…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Related questions

Question

W6Q2P1

Expert Solution

Step 1: Introduction.

Given information:

The parametric equations of three curves are shown below;

$i) x = - t^{2}, y = t + 6, - 4 \leq t \leq 4$

$i i) x = - t + 7, y = - 5 t - 5, - 5 \leq t \leq 5$

$i i i) x = 3 \cos t, y = 3 \sin 2 t, 0 \leq t \leq π$

To find:

For each set of parametric equations, find several points on the curve and sketch the curve.

Concept used:

Parametric equations represent a curve in terms of two or more parameters (usually $x$ and $y$ in terms of $t$ ).
We can find points on the curve by substituting different values of $t$ within the given range.

Formula Used:

Plug different values of $t$ within the specified range into the parametric equations to calculate corresponding $x$ and $y$ values.
Create a table of values for $t$ , $x$ , and $y$ to represent points on the curve.
Sketch the curve using the points obtained from the table.