Question 1

Simplify  if  .

Accepted Answer

The answer of Simplify  if  ....

Question 2

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. ​

Accepted Answer

A) The maximum velocity is 3.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is   seconds. 
B) The maximum velocity is 3.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is   seconds. 
C) The maximum velocity is 7 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is   seconds.. 
D) The maximum velocity is 7 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is   seconds. 
E) The maximum velocity is 2.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is   seconds.

Question 3

Evaluate without using a calculator.

Accepted Answer

The answer of Evaluate without using a calculator. ...

Question 4

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

Accepted Answer

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B) ​  
C) ​  
D) ​  
E) ​

Question 5

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

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Question 6

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 ​  ​

Accepted Answer

A) ​  
B) ​  
C) ​   ​  
D) ​  
E) ​

Question 7

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.  ​

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Question 8

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

Accepted Answer

A) ​ ​  ​  
B) ​  ​  
C) ​  ​  
D) ​  ​  
E) ​  ​

Question 9

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.  ​

Accepted Answer

A)   
B) ​  
C) ​  
D) ​  
E) ​

Question 10

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

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Question 11

Match between columns
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Accepted Answer

The Answer of cot x = 0 and sec x is...

Question 12

Evaluate without using a calculator.  ​ 
__________ °

Accepted Answer

The answer of Evaluate without using a calculator.  ​...

Question 13

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 .  ​

Accepted Answer

A) ​  
B) ​  
C) ​

Question 14

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

Accepted Answer

The answer of Evaluate the expression without using a calculator,...

Question 15

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

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Question 16

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. ​

Accepted Answer

A) The maximum value of I is 40 amperes; one complete cycle takes   seconds. 
B) The maximum value of I is 5 amperes; one complete cycle takes   seconds. 
C) The maximum value of I is 20 amperes; one complete cycle takes   seconds. 
D) The maximum value of I is 40 amperes; one complete cycle takes   seconds. 
E) The maximum value of I is 20 amperes; one complete cycle takes   seconds.

Question 17

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

Accepted Answer

The answer of Evaluate the expression without using a calculator,...

Question 18

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

Accepted Answer

The answer of Prove the identity. 
cos(- β )csc( -...

Question 19

Evaluate without using a calculator.

Accepted Answer

The answer of Evaluate without using a calculator. ...

Question 20

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 ​  ​

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Exam 4: Graphing and Inverse Functions

Simplify if .

Evaluate without using a calculator.

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

Identify the graph of the equation over the given interval.

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

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.

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

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.

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

Match each value of x below with the letter of the corresponding equation.

Evaluate without using a calculator. __________ °

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 .

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

Identify the graph of the equation over the given interval.

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

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

Evaluate without using a calculator.

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

Exam 4: Graphing and Inverse Functions

Simplify if .

Evaluate without using a calculator.

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

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

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 ​ ​

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. ​

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

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. ​

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

Match each value of x below with the letter of the corresponding equation.

Evaluate without using a calculator. ​ __________ °

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 . ​

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

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

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

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

Evaluate without using a calculator.

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

Identify the graph of the equation over the given interval.

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

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.

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

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.

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

Evaluate without using a calculator. __________ °

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 .

Identify the graph of the equation over the given interval.

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