(a)
To write: The given function in terms of first power of cosine.
(a)
Answer to Problem 129E
The given function in terms of first power of cosine can be written as:
Explanation of Solution
Given information:
The following function:
Formula used:
The following power reduction formula:
The following expansion formula:
Calculation:
The given function in terms of first power of cosine can be written as:
(b)
To write: The given function in another way.
(b)
Answer to Problem 129E
The given function in another way can be written as:
Explanation of Solution
Given information:
The following function:
Formula used:
The following power reduction formula:
The following expansion formula:
Calculation:
The given function in another way can be written as:
This can be verified graphically as:
Graph:
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expressions
Step 4: Press GRAPH button to graph the function.
The graph is obtained as:
Interpretation:
Since both the curves coincide, the equation is verified.
(c)
To write: The function after adding a trigonometric term so that it becomes a perfect square trinomial.
(c)
Answer to Problem 129E
The function after adding a trigonometric term so that it becomes a perfect square trinomial.
can be written as:
Explanation of Solution
Given information:
The following function:
Formula used:
The following expansion formula:
The following Pythagorean identity:
Calculation:
The given function can be written as a perfect square trinomial as follows:
This can be verified graphically as:
Graph:
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expressions
Step 4: Press GRAPH button to graph the function.
The graph is obtained as:
Interpretation:
Since both the curves coincide, the equation is verified.
(d)
To write: The result in part (c) as sine of double angle.
(d)
Answer to Problem 129E
The result in part (c) as sine of double anglecan be written as:
Explanation of Solution
Given information:
The following function:
Formula used:
The following double angle formula:
Calculation:
The result in part (c) as sine of double angle can be written as follows:
This can be verified graphically as:
Graph:
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expressions
Step 4: Press GRAPH button to graph the function.
The graph is obtained as:
Interpretation:
Since both the curves coincide, the equation is verified.
(e)
To explain: The given statement.
(e)
Answer to Problem 129E
No, it does not specifically mean that one of you is wrong.
Explanation of Solution
Given information:
The following statement:
When you rewrite a trigonometric expression, your result may not be the same as a friend. Does this mean that one of you is wrong?
If a friend’s answer is different than yours, it does not specifically mean that one of you is wrong. As seen in the different parts of this sum, a function can be written in many different ways. To verify if your answer is correct, the graphs of the two functions must coincide.
Chapter 5 Solutions
Precalculus with Limits: A Graphing Approach
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