Deck 29: Inverse Trigonometric Functions

Question 1

Use an inverse trigonometric function to write θ as a function of x.​ ​ a = x
B = 10
​

A)
B)
C)
D)
E)

Answer 1

Question 2

Use an inverse trigonometric function to write θ as a function of x.​ ​ a = x
B = 6
​

A)
B)
C)
D)
E)

Answer 2

Question 3

Evaluate the expression.Round your result to two decimal places.​ ​

A)2.12
B)0.12
C)1.12
D)-0.88
E)3.12

Answer 3

1.12

Question 4

Use an inverse trigonometric function to write θ as a function of x.​ ​ a = x + 5
B = 10
​

A)
B)
C)
D)
E)

Question 5

Use an inverse trigonometric function to write θ as a function of x.​ ​ a = x + 6
B = 2
​

A)
B)
C)
D)
E)

Question 6

Evaluate the expression.Round your result to two decimal places.​ ​

A)1.87
B)-2.13
C)-1.13
D)0.87
E)-0.13

Question 7

Evaluate the expression.Round your result to two decimal places.​ ​

A)3.54
B)0.54
C)1.54
D)2.54
E)-0.46

Question 8

Evaluate the expression.Round your result to two decimal places.​ ​

A)-0.66
B)2.34
C)1.34
D)3.34
E)0.34

Question 9

Use the properties of inverse trigonometric functions to evaluate the expression.​ ​

A)
B)
C)
D)
E)40

Question 10

Evaluate the expression.Round your result to two decimal places.​ ​

A)0.30
B)1.30
C)4.30
D)3.30
E)2.30

Question 11

Evaluate the expression.Round your result to two decimal places.​ ​

A)-1.53
B)-0.53
C)2.47
D)0.47
E)1.47

Question 12

Evaluate the expression.Round your result to two decimal places.​ ​

A)-3.53
B)0.47
C)-0.53
D)-1.53
E)-2.53

Question 13

Evaluate the expression.Round your result to two decimal places.​ ​

A)4.21
B)2.21
C)3.21
D)0.21
E)1.21

Question 14

Evaluate the expression.Round your result to two decimal places.​ ​

A)2.71
B)-0.29
C)1.71
D)0.71
E)-1.29

Question 15

Evaluate the expression.Round your result to two decimal places.​ ​

A)-0.53
B)-1.53
C)0.47
D)-3.53
E)-2.53

Question 16

Use the properties of inverse trigonometric functions to evaluate the expression.​ ​

A)
B)
C)0.4
D)
E)

Question 17

Use an inverse trigonometric function to write θ as a function of x.​ ​ a = 5x
B = x + 9
​

A)
B)
C)
D)
E)

Question 18

Use an inverse trigonometric function to write θ as a function of x.​ ​ ​

A)
B)
C)
D)
E)

Question 19

Evaluate the expression.Round your result to two decimal places.​ ​

A)1.73
B)-0.27
C)-1.27
D)2.73
E)0.73

Question 20

Evaluate the expression.Round your result to two decimal places.​ ​

A)2.20
B)0.20
C)3.20
D)-0.80
E)1.20

Question 21

An airplane flies at an altitude of miles toward a point directly over an observer.Consider θ and x as shown in the figure.Write θ as a function of x.​ ​

A)
B)
C)
D)
E)

Question 22

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 23

Find an algebraic expression that is equivalent to the expression..​ ​

A)
B)
C)
D)
E)

Question 24

Find an algebraic expression that is equivalent to the expression.​ ​

A)
B)
C)
D)
E)

Question 25

Find the value of the expression.Round your result to two decimal places.​ ​

A)0.28
B)1.28
C)1.29
D)-1.29
E)-0.28

Question 26

A television camera at ground level is filming the lift-off of a space shuttle at a point meters from the launch pad (see figure).Let θ be the angle of elevation to the shuttle and let s be the height of the shuttle.Write θ as a function of s.​ ​

A)
B)
C)
D)
E)

Question 27

A boat is pulled in by means of a winch located on a dock feet above the deck of the boat (see figure).Let θ be the angle of elevation from the boat to the winch and let s be the length of the rope from the winch to the boat.Write θ as a function of s.​ ​

A)
B)
C)
D)
E)

Question 28

Find the value of the expression.Round your result to two decimal places.​ ​

A)1.61
B)1.53
C)0.04
D)0.96
E)-0.04

Question 29

Use the properties of inverse trigonometric functions to evaluate .

A)
B)
C)
D)
E)

Question 30

A security car with its spotlight on is parked meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x.​ ​

A)
B)
C)
D)
E)

Question 31

Use a calculator to evaluate .Round your answer to two decimal places.

A)0.68
B)
C)0.72
D)
E)2.51

Question 32

Use the properties of inverse trigonometric functions to evaluate .

A)
B)
C)
D)
E)

Question 33

Use an inverse function to write θ as a function of x.

A)​
B)
C)
D)
E)

Question 34

Find the value of the expression.Round your result to two decimal places.​ ​

A)-1.32
B)1.83
C)-0.26
D)-1.26
E)0.74

Question 35

Use the properties of inverse trigonometric functions to evaluate the expression.​ ​

A)1
B)-1
C)
D)0
E)

Question 36

Use a calculator to evaluate .Round your answer to two decimal places.

A)1.25
B)0.58
C)0.32
D)1.40
E)0.76

Question 37

Find an algebraic expression that is equivalent to the expression..​ ​

A)
B)
C)
D)
E)

Question 38

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 39

Find the value of the expression.Round your result to two decimal places.​ ​

A)-1.25​
B)1.25
C)1.89
D)3.14
E)-3.14 ​

Question 40

Use an inverse function to write θ as a function of x.

A)
B)
C)
D)
E)

Question 41

Use a graphing utility to graph the function below.​ ​ π -π
Π -π

A)π​ -π​
B)π​ -π​
C)​ π​ -π​
D)π​ -π​
E)π​ -π​

Question 42

Find the exact value of .

A)
B)
C)
D)
E)

Question 43

Use a graphing utility to graph the function below.

A)
B)
C)
D)
E)

Question 44

Write an algebraic expression that is equivalent to .

A)
B)
C)
D)
E)

Question 45

Write an algebraic expression that is equivalent to .

A)
B)
C)
D)
E)

Question 46

A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile,θ,is called the angle of repose.If the height of a pile of sand is 14 feet and its diameter is approximately 47 feet,determine the angle of repose.Round your answer to the nearest degree.

A)
B)
C)
D)
E)

Question 47

Find the exact value of .

A)
B)
C)
D)
E)

Question 48

Which of the following functions is represented by the graph below?

A)
B)
C)
D)
E)

Question 49

Which of the following functions is represented by the graph below?

A)2arccos x
B)arcsin 2x
C)arccos (x + 1)
D)2arcsin
E)arccos

Question 50

Which of the following can be inserted to make the statement true?

A)
B)
C)
D)
E)x