Question 1

Evaluate the expression.Round your result to two decimal places.​ $$\arctan ~~2.6$$ ​

Accepted Answer

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

Question 2

Use an inverse trigonometric function to write θ as a function of x.​   ​ $\begin{array} { l } 
a = x ^ { 2 } - 16 \
b = x - 4
\end{array}$ ​

Accepted Answer

A)  $\theta = \arcsin \frac { 1 } { x + 4 } , x \neq 4$ 
B)  $\theta = \arctan \frac { 1 } { x - 4 } , x \neq 4$ 
C)  $\theta = \arctan \frac { 1 } { x + 4 } , x \neq 4$ 
D)  $\theta = \arccos \frac { 1 } { x + 4 } , x \neq 4$ 
E)  $\theta = \operatorname { arccot } \frac { 1 } { x + 4 } , x \neq 4$ 
A)  $\theta = \arcsin \frac { 1 } { x + 4 } , x \neq 4$ 
B)  $\theta = \arctan \frac { 1 } { x - 4 } , x \neq 4$ 
C)  $\theta = \arctan \frac { 1 } { x + 4 } , x \neq 4$ 
D)  $\theta = \arccos \frac { 1 } { x + 4 } , x \neq 4$ 
E)  $\theta = \operatorname { arccot } \frac { 1 } { x + 4 } , x \neq 4$

Question 3

A television camera at ground level is filming the lift-off of a space shuttle at a point $a = 925$ 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.​   ​

Accepted Answer

A)  $\theta = \arctan \frac { s } { 925 }$ 
B)  $\theta = \arcsin \frac { s } { 925 }$ 
C)  $\theta = \operatorname { arccsc } \frac { s } { 925 }$ 
D)  $\theta = \arctan \frac { 925 } { s }$ 
E)  $\theta = \operatorname { arccot } \frac { s } { 925 }$ 
A)  $\theta = \arctan \frac { s } { 925 }$ 
B)  $\theta = \arcsin \frac { s } { 925 }$ 
C)  $\theta = \operatorname { arccsc } \frac { s } { 925 }$ 
D)  $\theta = \arctan \frac { 925 } { s }$ 
E)  $\theta = \operatorname { arccot } \frac { s } { 925 }$

Question 4

A security car with its spotlight on is parked $a = 30$ meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x.​   ​

Accepted Answer

A)  $\theta = \operatorname { arccot } \frac { x } { 30 }$ 
B)  $\theta = \arctan \frac { x } { 30 }$ 
C)  $\theta = \operatorname { arccsc } \frac { x } { 30 }$ 
D)  $\theta = \arcsin \frac { x } { 30 }$ 
E)  $\theta = \arctan \frac { 30 } { x }$ 
A)  $\theta = \operatorname { arccot } \frac { x } { 30 }$ 
B)  $\theta = \arctan \frac { x } { 30 }$ 
C)  $\theta = \operatorname { arccsc } \frac { x } { 30 }$ 
D)  $\theta = \arcsin \frac { x } { 30 }$ 
E)  $\theta = \arctan \frac { 30 } { x }$

Question 5

Use the properties of inverse trigonometric functions to evaluate $$\tan [ \arctan ( - 0.11 ) ]$$ .

Accepted Answer

A)  $- 0.55$ 
B)  $0.12$ 
C)  $- 0.41$ 
D)  $- 0.11$ 
E)  $- 0.07$ 
A)  $- 0.55$ 
B)  $0.12$ 
C)  $- 0.41$ 
D)  $- 0.11$ 
E)  $- 0.07$

Question 6

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

Accepted Answer

A)  $\theta = \arctan \frac { x + 9 } { 5 x }$ 
B)  $\theta = \arcsin \frac { x + 9 } { 5 x }$ 
C)  $\theta = \operatorname { arcsec } \frac { x + 9 } { 5 x }$ 
D)  $\theta = \operatorname { arccsc } \frac { x + 9 } { 5 x }$ 
E)  $\theta = \arccos \frac { x + 9 } { 5 x }$ 
A)  $\theta = \arctan \frac { x + 9 } { 5 x }$ 
B)  $\theta = \arcsin \frac { x + 9 } { 5 x }$ 
C)  $\theta = \operatorname { arcsec } \frac { x + 9 } { 5 x }$ 
D)  $\theta = \operatorname { arccsc } \frac { x + 9 } { 5 x }$ 
E)  $\theta = \arccos \frac { x + 9 } { 5 x }$

Question 7

Use a graphing utility to graph the function below. $y = 2 \sin ^ { - 1 } ( 2 x ) + \frac { \pi } { 2 }$

Accepted Answer

A)  $$\frac { 3 \pi } { 2 }$$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
B)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
E)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
A)  $$\frac { 3 \pi } { 2 }$$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
B)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$ 
E)  $\frac { 3 \pi } { 2 }$   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 2 }$ $- \frac { \pi } { 2 }$

Question 8

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

Accepted Answer

A)  $\theta = \arctan \frac { x + 6 } { 2 }$ 
B)  $\theta = \arcsin \frac { 2 } { x + 6 }$ 
C)  $\theta = \operatorname { arccot } \frac { x + 6 } { 2 }$ 
D)  $\theta = \arccos \frac { x + 6 } { 2 }$ 
E)  $\theta = \arcsin \frac { x + 6 } { 2 }$ 
A)  $\theta = \arctan \frac { x + 6 } { 2 }$ 
B)  $\theta = \arcsin \frac { 2 } { x + 6 }$ 
C)  $\theta = \operatorname { arccot } \frac { x + 6 } { 2 }$ 
D)  $\theta = \arccos \frac { x + 6 } { 2 }$ 
E)  $\theta = \arcsin \frac { x + 6 } { 2 }$

Question 9

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.

Accepted Answer

A)  $27 ^ { \circ }$ 
B)  $29 ^ { \circ }$ 
C)  $28 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
E)  $31 ^ { \circ }$ 
A)  $27 ^ { \circ }$ 
B)  $29 ^ { \circ }$ 
C)  $28 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
E)  $31 ^ { \circ }$

Question 10

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

Accepted Answer

A) ​ $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x - 1 } \right)$ 
B)  $\theta = \tan ^ { - 1 } \left( \frac { x - 1 } { x + 1 } \right)$ 
C)  $\theta = \tan ^ { - 1 } ( x + 1 )$ 
D)  $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x ^ { 2 } + 1 } \right)$ 
E)  $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x + 1 } \right)$ 
A) ​ $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x - 1 } \right)$ 
B)  $\theta = \tan ^ { - 1 } \left( \frac { x - 1 } { x + 1 } \right)$ 
C)  $\theta = \tan ^ { - 1 } ( x + 1 )$ 
D)  $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x ^ { 2 } + 1 } \right)$ 
E)  $\theta = \tan ^ { - 1 } \left( \frac { 1 } { x + 1 } \right)$

Exam 29: Inverse Trigonometric Functions

Evaluate the expression.Round your result to two decimal places.​ arctan⁡ 2.6\arctan ~~2.6arctan 2.6 ​

Use an inverse trigonometric function to write θ as a function of x.​ ​ a=-16 b=x-4 ​

A television camera at ground level is filming the lift-off of a space shuttle at a point a=925a = 925a=925 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 security car with its spotlight on is parked a=30a = 30a=30 meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x.​ ​

Use the properties of inverse trigonometric functions to evaluate tan⁡[arctan⁡(−0.11)]\tan [ \arctan ( - 0.11 ) ]tan[arctan(−0.11)] .

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

Use a graphing utility to graph the function below. y=2sin⁡−1(2x)+π2y = 2 \sin ^ { - 1 } ( 2 x ) + \frac { \pi } { 2 }y=2sin−1(2x)+2π​

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

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

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

Evaluate the expression.Round your result to two decimal places. $\arctan ~~2.6$

Use an inverse trigonometric function to write θ as a function of x. $Use an inverse trigonometric function to write θ as a function of x. \begin{array} { l } a = x ^ { 2 } - 16 \\ b = x - 4 \end{array} $ a=-16 b=x-4

A television camera at ground level is filming the lift-off of a space shuttle at a point $a = 925$ 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 security car with its spotlight on is parked $a = 30$ meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x.

Use the properties of inverse trigonometric functions to evaluate $\tan [ \arctan ( - 0.11 ) ]$ .

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

Use a graphing utility to graph the function below. $y = 2 \sin ^ { - 1 } ( 2 x ) + \frac { \pi } { 2 }$

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