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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) t X у of values of t, x and y to find several points of the curve and then sketch the curve: i) x=- , y=t+6, ii) x = -t+7, y=-5t-5, iii) x = 3 cos 2t, y = 3 sin 2t, -4≤t≤4 -5 ≤ t ≤ 5 0≤t≤ π

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) t X у of values of t, x and y to find several points of the curve and then sketch the curve: i) x=- , y=t+6, ii) x = -t+7, y=-5t-5, iii) x = 3 cos 2t, y = 3 sin 2t, -4≤t≤4 -5 ≤ t ≤ 5 0≤t≤ π

Advanced Engineering Mathematics
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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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) t X y of 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≤4 ii) x = −t+7, y=-5t-5, iii) x = 3 cos 2t, y = 3 sin 2t, -5 ≤t≤5 0≤t≤ π
Transcribed Image Text: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) t X y of 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≤4 ii) x = −t+7, y=-5t-5, iii) x = 3 cos 2t, y = 3 sin 2t, -5 ≤t≤5 0≤t≤ π
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