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Q1. For the following parametric equations, (a) ㅠ x= = cos² t, y = 1 - sint, 0≤ t ≤ x = 1² +t, y=t²-t, -2 ≤ t ≤ 2, (b) (i) sketch the curve, (ii) convert the parametric equations of a curve into the Cartesian (rectangular) form, (iii) indicate the orientation of the curve, that is, the direction that a point moves on the curve as t is increasing.

Q1. For the following parametric equations, (a) ㅠ x= = cos² t, y = 1 - sint, 0≤ t ≤ x = 1² +t, y=t²-t, -2 ≤ t ≤ 2, (b) (i) sketch the curve, (ii) convert the parametric equations of a curve into the Cartesian (rectangular) form, (iii) indicate the orientation of the curve, that is, the direction that a point moves on the curve as t is increasing.

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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Q1. For the following parametric equations, (a) x = cos² t, y = 1 - sint, 0≤ t ≤2 x = 1² +t, y=t²-t, -2 ≤ t ≤ 2, (b) (i) sketch the curve, (ii) convert the parametric equations of a curve into the Cartesian (rectangular) form, (iii) indicate the orientation of the curve, that is, the direction that a point moves on the curve as t is increasing.
Transcribed Image Text:Q1. For the following parametric equations, (a) x = cos² t, y = 1 - sint, 0≤ t ≤2 x = 1² +t, y=t²-t, -2 ≤ t ≤ 2, (b) (i) sketch the curve, (ii) convert the parametric equations of a curve into the Cartesian (rectangular) form, (iii) indicate the orientation of the curve, that is, the direction that a point moves on the curve as t is increasing.
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