Chapter 12.1, Problem 12E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating a function In Exercises 11 and 12 evaluate the vector-valued function at each given value of t. r ( t ) = cos   t i   +  2 sin  t j (a) r ( 0 ) . (b) r ( π / 4 ) (c) r ( θ − π ) (d) r ( π / 6 + Δ t ) − r ( π / 6 )

To determine

To calculate: The value of the vector function r(t)=costi+2sintj at each of the given value t.

r(0)

r( π4)

r (θπ)

r(π6+Δt)- r(π6)

Explanation

Given: Vector function: r(t)=costi+2sintj

r(0)

r (Ï€4)

r (Î¸âˆ’Ï€)

r(Ï€6+Î”t)- r(Ï€6)

Calculation:

Consider t as 0, Ï€4,Î¸-Â Ï€ and Ï€ /6+Î”tÂ andÏ€/6 in order to determine the vector value:

r(0)=cos0i+2sin0j=i

r(Ï€/4)=cosÏ€4i+2sinÏ€4j=12i+2j

r(Î¸âˆ’Ï€)=cos(Î¸âˆ’Ï€)i+2sin(Î¸âˆ’Ï€)j=cos[âˆ’(Ï€âˆ’Î¸)]i+2sin[âˆ’(Ï€âˆ’Î¸)]=cos[(Ï€âˆ’Î¸)]iâˆ’2sin[(Ï€âˆ’Î¸)]j=âˆ’cosÎ¸iâˆ’

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