Concept explainers
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
where t is measured in days.
- (a) Find the period of R Leonis.
- (b) Find the maximum and minimum brightness.
- (c) Graph the function b.
a.
To find: The period of R Leonis.
Answer to Problem 80E
The period of the function
Explanation of Solution
Given:
The function
Cosine curve:
The cosine curve
Calculation:
The period of the function
Therefore, the period of the function
b.
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
That is, the maximum point is 1 and minimum point is
Thus, the range of the cosine function
The maximum and minimum brightness is computed as follows,
Take
Take
Therefore, the maximum and minimum brightness are 10 and 5.8.
c.
To sketch: The graph of the function b.
Explanation of Solution
Use the online graphing calculator and draw the graph of the function
From Figure 1, it is observed that the maximum and minimum brightness are 10 and 5.8. The range of the function is
Chapter 5 Solutions
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