Explanation Given: The vector valued function: r ( t ) = 10 cos t i + 10 sin t j , in the interval [ 0 , 2 π ] . Graph: The given vector valued function is r ( t ) = 10 cos t i + 10 sin t j ..…. (1) Now we find the vector valued function over the given interval [ 0 , 2 π ] . r ( 0 ) = 10 i + 0 j .….. (2) r ( 2 π ) = 10 i + 0 j ..…. (3) From (2) and (3), there are two end points on the graph of the given function as ( 10 , 0 ) and ( 10 , 0 ) . In the parametric form, the vector function can be written as: x = 10 cos t y = 10 sin t Now, square the x , and y and add it. x 2 + y 2 = 100 ( cos 2 t + sin 2 t ) ( x − 0 ) 2 + ( y − 0 ) 2 = ( 10 ) 2 y = ± 100 − x 2 It is the general equation of circle of radius 10 units, and center is at origin

Calculus: Early Transcendental Functions

7th Edition

ISBN: 9781337552516

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Question

Chapter 12, Problem 58RE

To determine

To graph: The plane curve over the given interval and the length of the curve of the position vector valued function r(t)=10costi+10sintj, in the interval [0,2π].

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Chapter 12, Problem 57RE

Chapter 12, Problem 59RE

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Chapter 12 Solutions

Calculus: Early Transcendental Functions

Ch. 12.1 - CONCEPT CHECK Vector-Valued Function Describe how...Ch. 12.1 - Prob. 2E Ch. 12.1 - Finding the domain In exercises 3-10 find the...Ch. 12.1 - Prob. 4E Ch. 12.1 - Finding the domain In exercises 3-10 find the...Ch. 12.1 - Finding the domain In exercises 3-10 find the...Ch. 12.1 - Finding the Domain In Exercises 3-10, find the...Ch. 12.1 - Finding the Domain In Exercises 3-10, find the...Ch. 12.1 - Prob. 9E Ch. 12.1 - Finding the domain In exercises 3-10 find the...

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To graph: The plane curve over the given interval and the length of the curve of the position vector valued function r ( t ) = 10 cos t i + 10 sin t j , in the interval [ 0 , 2 π ] .

Solution Summary: The author describes the vector valued function r(t)=10mathrmcosti+10

Concept explainers

To graph: The plane curve over the given interval and the length of the curve of the position vector valued function r(t)=10costi+10sintj, in the interval [0,2π].

Want to see the full answer?

Chapter 12 Solutions