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The circle æ² + (y– 1)² = 4 has center (0, 1) and radius 2, so by Example 4 it can be represented by æ = 2 cos t, y = 1+2 sin t, 0 st< 2m. This representation gives us the circle with a counterclockwise orientation starting at (2, 1). (a) To get a clockwise orientation, we could change the equations to æ = 2 cos t, y = 1 – 2 sin t, 0

The circle æ² + (y– 1)² = 4 has center (0, 1) and radius 2, so by Example 4 it can be represented by æ = 2 cos t, y = 1+2 sin t, 0 st< 2m. This representation gives us the circle with a counterclockwise orientation starting at (2, 1). (a) To get a clockwise orientation, we could change the equations to æ = 2 cos t, y = 1 – 2 sin t, 0

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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#33 2D. PLEASE COME THROUGH!!

33. The circle æ² + (y – 1)² = 4 has center (0, 1) and radius 2, so by Example 4 it can be represented by æ = 2 cos t, y = 1+2 sin t, 0<t< 2n. This representation gives us the circle with a counterclockwise orientation starting at (2, 1). (a) To get a clockwise orientation, we could change the equations to æ = 2 cos t, y = 1 – 2 sin t, 0 < t < 2n. (b) To get three times around in the counterclockwise direction, we use the original equations æ = 2 cos t, y = 1+2 sint with the domain expanded to 0 <t < 6n. (c) To start at (0,3) using the original equations, we must have æ1 = 0; that is, 2 cos t = 0. Hence, t = . So we use x = 2 cos t, y = 1+2 sin t, <t S Alternatively, if we want t to start at 0, we could change the equations of the curve. For example, we could use x = -2 sin t, y =1+2 cos t, 0 <t< r.
Transcribed Image Text:33. The circle æ² + (y – 1)² = 4 has center (0, 1) and radius 2, so by Example 4 it can be represented by æ = 2 cos t, y = 1+2 sin t, 0<t< 2n. This representation gives us the circle with a counterclockwise orientation starting at (2, 1). (a) To get a clockwise orientation, we could change the equations to æ = 2 cos t, y = 1 – 2 sin t, 0 < t < 2n. (b) To get three times around in the counterclockwise direction, we use the original equations æ = 2 cos t, y = 1+2 sint with the domain expanded to 0 <t < 6n. (c) To start at (0,3) using the original equations, we must have æ1 = 0; that is, 2 cos t = 0. Hence, t = . So we use x = 2 cos t, y = 1+2 sin t, <t S Alternatively, if we want t to start at 0, we could change the equations of the curve. For example, we could use x = -2 sin t, y =1+2 cos t, 0 <t< r.
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