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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaa299df-cb1e-4822-92c5-78198cbb1864%2F9cc4e3ed-28b2-4a1e-8480-166641a1bca7%2Fpb7a1qk_processed.png&w=3840&q=75)
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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