Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 5.3, Problem 80E

Variable Stars Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modeled by the function

b ( t ) = 7.9 − 2.1 cos ( π 156 t )

where t is measured in days.

  1. (a) Find the period of R Leonis.
  2. (b) Find the maximum and minimum brightness.
  3. (c) Graph the function b.

Chapter 5.3, Problem 80E, Variable Stars Variable stars are ones whose brightness varies periodically. One of the most visible

a.

Expert Solution
Check Mark
To determine

To find: The period of R Leonis.

Answer to Problem 80E

The period of the function b(t)=7.9−2.1cos(π156t) is 312 .

Explanation of Solution

Given:

The function b(t)=7.9−2.1cos(π156t) .

Cosine curve:

The cosine curve y=acoskx (k>0) have amplitude |a| and period 2πk .

Calculation:

The period of the function b(t)=7.9−2.1cos(π156t) is computed as follows,

2πk=2ππ156    (k=160π)=312

Therefore, the period of the function b(t)=7.9−2.1cos(π156t) is 312 .

b.

Expert Solution
Check Mark
To determine

To find: The maximum and minimum brightness.

Answer to Problem 80E

The maximum and minimum brightness are 10 and 5.8.

Explanation of Solution

Calculation:

Note that, the range of the cosine function f(x)=cosx is −1≤cosx≤1 .

That is, the maximum point is 1 and minimum point is −1 .

Thus, the range of the cosine function cos(π156t) is −1≤cos(π156t)≤1 .

The maximum and minimum brightness is computed as follows,

Take cos(π156t)=1 , then

b(t)=7.9−2.1(1)=7.9−2.1=5.8

Take cos(π156t)=−1 , then

b(t)=7.9−2.1(−1)=7.9+2.1=10

Therefore, the maximum and minimum brightness are 10 and 5.8.

c.

Expert Solution
Check Mark
To determine

To sketch: The graph of the function b.

Explanation of Solution

Use the online graphing calculator and draw the graph of the function b(t)=7.9−2.1cos(π156t) as shown in below Figure 1.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5.3, Problem 80E

From Figure 1, it is observed that the maximum and minimum brightness are 10 and 5.8. The range of the function is [5.8,10] .

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Chapter 5.3, Problem 79E
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Chapter 5.3, Problem 81E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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