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Exam 4: Graphing and Inverse Functions

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Exam 1: The Six Trigonometric Functions158 Questionsadd course
Exam 2: Right Triangle Trigonometry181 Questionsadd course
Exam 3: Radian Measure157 Questionsadd course
Exam 4: Graphing and Inverse Functions156 Questionsadd course
Exam 5: Identities and Formulas186 Questionsadd course
Exam 6: Equations134 Questionsadd course
Exam 7: Triangles225 Questionsadd course
Exam 8: Complex Numbers and Polar Coordinates177 Questionsadd course
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Simplify Simplify if . if Simplify if . .

(Short Answer)
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Question 101

A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v of the weight at any time t is given by the equation v = 3.5sin 4 πt where v is measured in meters per second and t is measured in seconds. Find the maximum velocity of the weight and the amount of time it takes for the weight to move from its lowest position to its highest position. ​

(Multiple Choice)
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Question 102

Evaluate without using a calculator. Evaluate without using a calculator.

(Essay)
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Question 103

For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph  on the same coordinate system. ​  on the same coordinate system. For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph  on the same coordinate system. ​ ​

(Multiple Choice)
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Question 104

Identify the graph of the equation over the given interval. Identify the graph of the equation over the given interval. ​ ​

(Multiple Choice)
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Question 105

The periods for The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​  and The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​  are π . The graphs of The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​ and The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​  will have periods The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​  and phase shifts The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​ , for The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​ Use these facts to identify the graph of the function ​ The periods for  and  are π . The graphs of and  will have periods  and phase shifts , for Use these facts to identify the graph of the function ​ ​ ​

(Multiple Choice)
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Question 106

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​ ​

(Multiple Choice)
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Question 107

Graph one complete cycle of the graph. Label the axes accurately and identify the period. Graph one complete cycle of the graph. Label the axes accurately and identify the period. ​ ​

(Multiple Choice)
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Question 108

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​ ​

(Multiple Choice)
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Question 109

Use addition of y -coordinates to sketch the graph of the function between Use addition of y -coordinates to sketch the graph of the function between  and . ​  and Use addition of y -coordinates to sketch the graph of the function between  and . ​ . Use addition of y -coordinates to sketch the graph of the function between  and . ​ ​

(Multiple Choice)
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Question 110
Match each value of x below with the letter of the corresponding equation.
Premises:
Responses:
cot x = 0
sec x = -1
Correct Answer:
Verified
Premises:
Responses:
cot x = 0
(Matching)
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Question 111

Evaluate without using a calculator. Evaluate without using a calculator. ​ __________ ° ​ __________ °

(Short Answer)
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Question 112

Sketch the graph of y = cos  x  between x = -4 π  and x  =  4 π  by extending the graph for x between 0 and 2 π . Sketch the graph of y = cos  x  between x = -4 π  and x  =  4 π  by extending the graph for x between 0 and 2 π . ​ ​

(Multiple Choice)
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Question 113

Evaluate the expression without using a calculator, and write your answer in radians. Evaluate the expression without using a calculator, and write your answer in radians.

(Essay)
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Question 114

Identify the graph of the equation over the given interval. Identify the graph of the equation over the given interval. ​ ​

(Multiple Choice)
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Question 115

The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and t represents time, then the relationship between I and t is given by I = 20cos 160 πt where I is measured in amperes and t is measured in seconds. Find the maximum value of I and the time it takes for I to go through one complete cycle. ​

(Multiple Choice)
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Question 116

Evaluate the expression without using a calculator, and write your answer in radians. Evaluate the expression without using a calculator, and write your answer in radians.

(Short Answer)
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Question 117

Prove the identity. cos(- β )csc( - β )tan( - β )= 1

(Essay)
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Question 118

Evaluate without using a calculator. Evaluate without using a calculator.

(Short Answer)
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Question 119

The periods for The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ and The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ are π . The graphs of The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ and The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​  will have periods  The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​  and phase shifts The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ , for The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ Use these facts to identify the graph of the function ​ The periods for and are π . The graphs of and  will have periods   and phase shifts , for Use these facts to identify the graph of the function ​ ​ ​

(Multiple Choice)
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Question 120
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