Question 1

Sketch the graph of the function   ​

Accepted Answer

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

Question 2

Find the period of the trigonometric function. ​   ​

Accepted Answer

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

Question 3

Find the indefinite integral of the following function. ​   ​

Accepted Answer

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

Question 4

From the given function   ,find the following trigonometric function.   ​   ​

Accepted Answer

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

Question 5

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 6

Find   given that   and   ​

Accepted Answer

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

Question 7

A guy wire is stretched from a broadcasting tower at a point 250 feet above the ground to an anchor 150 feet from the base (see figure).How long is the wire? ​   ​   ​

Accepted Answer

A)  291.55 feet 
B)  193.65 feet 
C)  150.83 feet 
D)  412.31 feet 
E)  244.95 feet 
A)  291.55 feet 
B)  193.65 feet 
C)  150.83 feet 
D)  412.31 feet 
E)  244.95 feet

Question 8

Determine the quadrant in which   lies if sinθ0. ​

Accepted Answer

A)  fourth quadrant 
B)  third quadrant 
C)  first quadrant 
D)  second quadrant 
E)  second or third quadrants 
A)  fourth quadrant 
B)  third quadrant 
C)  first quadrant 
D)  second quadrant 
E)  second or third quadrants

Question 9

A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure). ​   ​
For a circle of radius r the area A of a sector of the circle with central angle θ (measured in radians)is given by   A sprinkler system on a farm is set to spray water over a distance of 70 feet and rotates through an angle of 90°.Use the above given information to find the area of the region.Round your answer to two decimal places.
​

Accepted Answer

A)  3,848.45 
B)  1,225.00 
C)  2,348.45 
D)  5,348.45 
E)  7,696.90 
A)  3,848.45 
B)  1,225.00 
C)  2,348.45 
D)  5,348.45 
E)  7,696.90

Question 10

Evaluate the definite integral   ​

Accepted Answer

A)  9 
B)  -9 
C)    
D)    
E)  ∞ 
A)  9 
B)  -9 
C)    
D)    
E)  ∞

Question 11

Solve the triangle for the indicated side. ​   ​   ​

Accepted Answer

A)  ​​side h​:   
B)  ​ ​​​side h​:   
C)  ​side h​:   
D)  ​​side h​:   ​ 
E)  ​​​​side h​:   
A)  ​​side h​:   
B)  ​ ​​​side h​:   
C)  ​side h​:   
D)  ​​side h​:   ​ 
E)  ​​​​side h​:

Question 12

Find the cosine of θ. ​   ​
​   ​

Accepted Answer

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

Question 13

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 14

Evaluate the definite integral. ​   ​

Accepted Answer

A)  -5 
B)  ​7 
C)  0 
D)  undefined 
E)  10 
A)  -5 
B)  ​7 
C)  0 
D)  undefined 
E)  10

Question 15

A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer. ​

Accepted Answer

A)  1,004 
B)  1,577 
C)  402 
D)  502 
E)  251 
A)  1,004 
B)  1,577 
C)  402 
D)  502 
E)  251

Question 16

Determine the relative extrema of the function   on the interval   ​ ​

Accepted Answer

A)  relative minimum:  
Relative maximum:   
B)  relative minimum:  
Relative maximum:   
C)  relative minimum:  
​relative maximum:   
D)  relative minimum:  
Relative maximum:   
E)  relative minimum:  
Relative maximum:   
A)  relative minimum:  
Relative maximum:   
B)  relative minimum:  
Relative maximum:   
C)  relative minimum:  
​relative maximum:   
D)  relative minimum:  
Relative maximum:   
E)  relative minimum:  
Relative maximum:

Question 17

Find the period and amplitude of the function   ​   ​

Accepted Answer

A)  Period: 2π; Amplitude: 3 
B)  Period: 2π; Amplitude:   
C)  Period: 2; Amplitude:   
D)  Period: 4; Amplitude: 3 
E)  Period: 4; Amplitude:   
A)  Period: 2π; Amplitude: 3 
B)  Period: 2π; Amplitude:   
C)  Period: 2; Amplitude:   
D)  Period: 4; Amplitude: 3 
E)  Period: 4; Amplitude:

Question 18

Find two values of θ that satisfy the equation below.Give values of θ in radians   Do not use a calculator. ​

Accepted Answer

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

Question 19

Find the cosine of θ. ​   ​   ​

Accepted Answer

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

Question 20

Find the radian measure of the given angle. ​   ​

Accepted Answer

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

Sketch the graph of the function

Find the period of the trigonometric function.

Find the indefinite integral of the following function.

From the given function ,find the following trigonometric function.

Find the indefinite integral.

Find given that and

A guy wire is stretched from a broadcasting tower at a point 250 feet above the ground to an anchor 150 feet from the base (see figure).How long is the wire?

Determine the quadrant in which lies if sinθ<0 and cosθ>0.

Evaluate the definite integral

Solve the triangle for the indicated side.

Find the cosine of θ.

Find the indefinite integral.

Evaluate the definite integral.

A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer.

Determine the relative extrema of the function on the interval

Find the period and amplitude of the function

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator.

Find the cosine of θ.

Find the radian measure of the given angle.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 8: Trigonometric Functions

Sketch the graph of the function ​

Find the period of the trigonometric function. ​ ​

Find the indefinite integral of the following function. ​ ​

From the given function ,find the following trigonometric function. ​ ​

Find the indefinite integral. ​ ​

Find given that and ​

A guy wire is stretched from a broadcasting tower at a point 250 feet above the ground to an anchor 150 feet from the base (see figure).How long is the wire? ​ ​ ​

Determine the quadrant in which lies if sinθ<0 and cosθ>0. ​

Evaluate the definite integral ​

Solve the triangle for the indicated side. ​ ​ ​

Find the cosine of θ. ​ ​ ​ ​

Find the indefinite integral. ​ ​

Evaluate the definite integral. ​ ​

A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer. ​

Determine the relative extrema of the function on the interval ​ ​

Find the period and amplitude of the function ​ ​

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator. ​

Find the cosine of θ. ​ ​ ​

Find the radian measure of the given angle. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Sketch the graph of the function

Find the period of the trigonometric function.

Find the indefinite integral of the following function.

From the given function ,find the following trigonometric function.

Find the indefinite integral.

Find given that and

A guy wire is stretched from a broadcasting tower at a point 250 feet above the ground to an anchor 150 feet from the base (see figure).How long is the wire?

Determine the quadrant in which lies if sinθ<0 and cosθ>0.

Evaluate the definite integral

Solve the triangle for the indicated side.

Find the cosine of θ.

Find the indefinite integral.

Evaluate the definite integral.

A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer.

Determine the relative extrema of the function on the interval

Find the period and amplitude of the function

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator.

Find the cosine of θ.

Find the radian measure of the given angle.