Exam 4: Graphing and Inverse Functions

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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.

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Match each value of x below with the letter of the corresponding equation.
Premises:
Responses:
sin x = 0
sin x = -1
Correct Answer:
Verified
Premises:
Responses:
sin x = 0
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For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph y = sin x on the same coordinate system. For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph y = sin x on the same coordinate system.   ​

(Multiple Choice)
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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.

(Essay)
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Sketch the graph of the equation from Sketch the graph of the equation from    to   .   ​  to Sketch the graph of the equation from    to   .   ​ . Sketch the graph of the equation from    to   .   ​

(Multiple Choice)
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Graph one complete cycle of Graph one complete cycle of   . Label the axes accurately. ​ . Label the axes accurately. ​

(Multiple Choice)
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If If   , find cos (- θ ). ​ , find cos (- θ ). ​

(Multiple Choice)
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Sketch one complete cycle of the following function by first graphing the appropriate sine or cosine curve and then using the reciprocal relationships. Sketch one complete cycle of the following function by first graphing the appropriate sine or cosine curve and then using the reciprocal relationships.   ​

(Multiple Choice)
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Identify the graph of Identify the graph of   ​

(Multiple Choice)
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Use your graphing calculator to graph the function between Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​  and Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​ . Show the graph of Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​ , Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​ , and Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​ . (Make sure your calculator is set to radian mode.)​ Use your graphing calculator to graph the function between    and   . Show the graph of   ,   , and   . (Make sure your calculator is set to radian mode.)​   ​

(Multiple Choice)
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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.

(Essay)
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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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Use your graphing calculator to graph the pair of functions for Use your graphing calculator to graph the pair of functions for    together on a single coordinate system. (Make sure your calculator is set to radian mode.)   ​  together on a single coordinate system. (Make sure your calculator is set to radian mode.) Use your graphing calculator to graph the pair of functions for    together on a single coordinate system. (Make sure your calculator is set to radian mode.)   ​

(Multiple Choice)
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Simplify Simplify   if    . if  Simplify   if    . .

(Short Answer)
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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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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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Use the graph of the equation Use the graph of the equation    shown below to identify the graph of one complete cycle of the equation   .   ​  shown below to identify the graph of one complete cycle of the equation Use the graph of the equation    shown below to identify the graph of one complete cycle of the equation   .   ​ . Use the graph of the equation    shown below to identify the graph of one complete cycle of the equation   .   ​

(Multiple Choice)
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Identify the graph of the function. y = cos 3 x ​

(Multiple Choice)
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Find all values of x for which the following is true. sin x = 1 ​

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For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. In each case, graph y = cos x on the same coordinate system. For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. In each case, graph y = cos x on the same coordinate system.   ​

(Multiple Choice)
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