vector a(t) = (cost, sint) with compone varies, the components of a(t) change as vectors a(0) and a(77) in component for the magnitude ||a(t)|| of vector a(t) rem: 5, show that the terminal point of vector adius 1.

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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Consider the vector a(t) = (cost, sint) with components that depend on a real number 1. As
the number t varies, the components of a(t) change as well, depending on the functions that
define them.
a. Write the vectors a(0) and a(7) in component form.
b. Show that the magnitude ||a(t)|| of vector a(t) remains constant for any real number t.
c. As t varies, show that the terminal point of vector a(t) describes a circle centered at the
origin of radius 1.
Transcribed Image Text:Consider the vector a(t) = (cost, sint) with components that depend on a real number 1. As the number t varies, the components of a(t) change as well, depending on the functions that define them. a. Write the vectors a(0) and a(7) in component form. b. Show that the magnitude ||a(t)|| of vector a(t) remains constant for any real number t. c. As t varies, show that the terminal point of vector a(t) describes a circle centered at the origin of radius 1.
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