Equal area property Consider the ellipse r(t) = (a cos t, b sin t), for 0 sts 27, where a and b are real numbers. Let 0 be the angle between the position vector and the x-axis. b a. Show that tan 0 = - tan t. a b. Find 0'(t). c. Recall that the area bounded by the polar curve r = on the interval [0, 0] is A(0) = "F(u))² đu. Letting f(0) f(0(1)) = |r(0(1))|, show that A'(t) = ab. d. Conclude that as an object moves around the ellipse, it sweeps out equal areas in equal times.
Equal area property Consider the ellipse r(t) = (a cos t, b sin t), for 0 sts 27, where a and b are real numbers. Let 0 be the angle between the position vector and the x-axis. b a. Show that tan 0 = - tan t. a b. Find 0'(t). c. Recall that the area bounded by the polar curve r = on the interval [0, 0] is A(0) = "F(u))² đu. Letting f(0) f(0(1)) = |r(0(1))|, show that A'(t) = ab. d. Conclude that as an object moves around the ellipse, it sweeps out equal areas in equal times.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Equal area property Consider the ellipse r(t) = (a cos t, b sin t),
for 0 sts 27, where a and b are real numbers. Let 0 be the
angle between the position vector and the x-axis.
b
a. Show that tan 0 = - tan t.
a
b. Find 0'(t).
c. Recall that the area bounded by the polar curve r =
on the interval [0, 0] is A(0) = "F(u))² đu. Letting
f(0)
f(0(1)) = |r(0(1))|, show that A'(t) = ab.
d. Conclude that as an object moves around the ellipse, it sweeps
out equal areas in equal times.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3332197-1afb-43da-b404-e9fe46f88079%2F6bcdbf0d-b8fb-4260-a9ea-a46475a9d715%2Fik5tgp.png&w=3840&q=75)
Transcribed Image Text:Equal area property Consider the ellipse r(t) = (a cos t, b sin t),
for 0 sts 27, where a and b are real numbers. Let 0 be the
angle between the position vector and the x-axis.
b
a. Show that tan 0 = - tan t.
a
b. Find 0'(t).
c. Recall that the area bounded by the polar curve r =
on the interval [0, 0] is A(0) = "F(u))² đu. Letting
f(0)
f(0(1)) = |r(0(1))|, show that A'(t) = ab.
d. Conclude that as an object moves around the ellipse, it sweeps
out equal areas in equal times.
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