Concept explainers
a.
Complete the table.
a.
Answer to Problem 87E
Explanation of Solution
Given information:
Complete the table.
Calculation:
By using calculator following function can be evaluated as follows
Co-functions of complementary angles are equal. If
The value of other functions can be found as follows
b.
Discuss the behaviour of the sine function for
b.
Answer to Problem 87E
The sine function covers its minimum value and maximum value in the given interval.
Explanation of Solution
Given information:
Discuss the behaviour of the sine function for
Calculation:
From the table, it can be seen that sine function is increasing from
Hence, the sine function covers its minimum value and maximum value in the given interval.
c.
Discuss the behaviour of the cosine function for
c.
Answer to Problem 87E
The cosine function covers its minimum value and maximum value in the given interval.
Explanation of Solution
Given information:
Discuss the behaviour of the cosine function for
Calculation:
From the table, it can be seen that cosine function is decreasing from
Hence, the cosine function covers its minimum value and maximum value in the given interval.
d.
Use the definitions of the sine and cosine functions to explain the results of parts (b) and (c).
d.
Answer to Problem 87E
The ration of opposite side of hepotenuse increase and so it can be deduced that sine function is increasing in the interval
The ration of adjacent side to hypotenuse decreases and so it can be deduced that cosine function is decreasing in the interval
Explanation of Solution
Given information:
Use the definitions of the sine and cosine functions to explain the results of parts (b) and (c).
Calculation:
Definition of sine function states that it is the ratio of opposite side and hypotenuse . As angle varies from
Definition of cosine function states that it is the ratio of adjacent side and hypotenuse. As angle varies from
Chapter 4 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning