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The circle of radius 1 has circumference 27. The arc length of this circle of radius 1, c(t) = (1+ cos 0, –1+ sin 0), for 0 = -10 to 0 = 10 is not 27. Why? O When the circle is below the x-axis, the contributions to the arc length are negative. O 10 – -10 = 20 radians goes around the circle a little more than 3 times, so we expect to get an arc length of 20, a little more than 3 · 27. O Framing challenge: You actually do get 27 for the arc length. O You only get the correct arc length if O runs from 0 to 277.

The circle of radius 1 has circumference 27. The arc length of this circle of radius 1, c(t) = (1+ cos 0, –1+ sin 0), for 0 = -10 to 0 = 10 is not 27. Why? O When the circle is below the x-axis, the contributions to the arc length are negative. O 10 – -10 = 20 radians goes around the circle a little more than 3 times, so we expect to get an arc length of 20, a little more than 3 · 27. O Framing challenge: You actually do get 27 for the arc length. O You only get the correct arc length if O runs from 0 to 277.

Calculus: Early Transcendentals
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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The circle of radius 1 has circumference 27. The arc length of this circle of radius 1, c(t) = (1+ cos 0, –1+ sin 0), for 0 = -10 to 0 = 10 is not 27. Why? O When the circle is below the x-axis, the contributions to the arc length are negative. O 10 – -10 = 20 radians goes around the circle a little more than 3 times, so we expect to get an arc length of 20, a little more than 3 · 27. O Framing challenge: You actually do get 27 for the arc length. O You only get the correct arc length if O runs from 0 to 277.
Transcribed Image Text:The circle of radius 1 has circumference 27. The arc length of this circle of radius 1, c(t) = (1+ cos 0, –1+ sin 0), for 0 = -10 to 0 = 10 is not 27. Why? O When the circle is below the x-axis, the contributions to the arc length are negative. O 10 – -10 = 20 radians goes around the circle a little more than 3 times, so we expect to get an arc length of 20, a little more than 3 · 27. O Framing challenge: You actually do get 27 for the arc length. O You only get the correct arc length if O runs from 0 to 277.
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