Question 1

Evaluate the expression.Round your result to two decimal places.​ $$\arcsin 0.45$$ ​

Accepted Answer

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

Question 2

Evaluate the expression.Round your result to two decimal places.​ $$\tan ^ { - 1 } \left( - \frac { 97 } { 4 } \right)$$ ​

Accepted Answer

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

Question 3

Evaluate the expression.Round your result to two decimal places.​ $$\arccos \left( - \frac { 2 } { 3 } \right)$$ ​

Accepted Answer

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

Question 4

Evaluate $\tan ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)$ without using a calculator.

Accepted Answer

A)  $- \frac { 5 \pi } { 6 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { 3 \pi } { 4 }$ 
E)  $- \frac { 2 \pi } { 3 }$ 
A)  $- \frac { 5 \pi } { 6 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { 3 \pi } { 4 }$ 
E)  $- \frac { 2 \pi } { 3 }$

Question 5

Evaluate the expression.Round your result to two decimal places.​ $$\cos ^ { - 1 } 0.44$$ ​

Accepted Answer

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

Question 6

Evaluate the expression.Round your result to two decimal places.​ $$\sin ^ { - 1 } 0.65$$ ​

Accepted Answer

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

Question 7

Which of the following can be inserted to make the statement true? $$\arccos \left( \frac { \sqrt { 36 - x ^ { 2 } } } { 6 } \right) = \arcsin ( \quad ) , 0 \leq x \leq 6$$

Accepted Answer

A)  $$\frac { x ^ { 2 } } { 6 }$$ 
B)  $$\frac { x } { 6 }$$ 
C)  $36 - x ^ { 2 }$ 
D)  $\frac { \sqrt { 72 - x ^ { 2 } } } { x }$ 
E) x 
A)  $$\frac { x ^ { 2 } } { 6 }$$ 
B)  $$\frac { x } { 6 }$$ 
C)  $36 - x ^ { 2 }$ 
D)  $\frac { \sqrt { 72 - x ^ { 2 } } } { x }$ 
E) x

Question 8

Evaluate the expression.Round your result to two decimal places.​ $$\arctan 30$$ ​

Accepted Answer

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

Question 9

Evaluate the expression.Round your result to two decimal places.​ $$\arccos 0.23$$ ​

Accepted Answer

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

Question 10

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

Accepted Answer

A)  $\theta = \arctan \frac { \sqrt { x ^ { 2 } - 9 } } { 3 }$ 
B)  $\theta = \arctan \frac { 3 } { x }$ 
C)  $\theta = \arctan \frac { 3 \pi } { x }$ 
D)  $\theta = \arctan \frac { \sqrt { x ^ { 2 } + 9 } } { 3 }$ 
E)  $\theta = \arctan \frac { x } { 3 }$ 
A)  $\theta = \arctan \frac { \sqrt { x ^ { 2 } - 9 } } { 3 }$ 
B)  $\theta = \arctan \frac { 3 } { x }$ 
C)  $\theta = \arctan \frac { 3 \pi } { x }$ 
D)  $\theta = \arctan \frac { \sqrt { x ^ { 2 } + 9 } } { 3 }$ 
E)  $\theta = \arctan \frac { x } { 3 }$

Question 11

Evaluate the expression.Round your result to two decimal places.​ $$\arcsin ( - 0.130 )$$ ​

Accepted Answer

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

Question 12

Evaluate the expression.Round your result to two decimal places.​ $$\arcsin \frac { 2 } { 3 }$$ ​

Accepted Answer

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

Question 13

Evaluate $\arctan \frac { \sqrt { 3 } } { 3 }$ without using a calculator.

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$ 
E)  $- \frac { 3 \pi } { 4 }$ 
A)  $\frac { \pi } { 6 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$ 
E)  $- \frac { 3 \pi } { 4 }$

Question 14

Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$ .

Accepted Answer

A)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 3 x }$ 
B)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
C)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 1 - 9 x ^ { 2 } }$ 
D)  $\frac { 1 } { 3 x }$ 
E)  $3 x$ 
A)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 3 x }$ 
B)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
C)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 1 - 9 x ^ { 2 } }$ 
D)  $\frac { 1 } { 3 x }$ 
E)  $3 x$

Question 15

An airplane flies at an altitude of $a = 6$ miles toward a point directly over an observer.Consider θ and x as shown in the figure.Write θ as a function of x.​   ​

Accepted Answer

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

Question 16

Use the properties of inverse trigonometric functions to evaluate $$\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]$$ .

Accepted Answer

A)  $\frac { \pi } { 5 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { 5 \pi } { 2 }$ 
D)  $\frac { 2 \pi } { 5 }$ 
E)  $- \frac { 3 \pi } { 5 }$ 
A)  $\frac { \pi } { 5 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { 5 \pi } { 2 }$ 
D)  $\frac { 2 \pi } { 5 }$ 
E)  $- \frac { 3 \pi } { 5 }$

Question 17

Use a graphing utility to graph the function below.​ $y = 2 \arcsin ( 2 x )$ ​ π $- 1$ $1$ $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π
Π $- 1$ $1$ $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π

Accepted Answer

A) π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
B) π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
C) ​ π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
D) π​   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π​ 
E) π​   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π​ 
A) π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
B) π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
C) ​ π​   $$\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$$ -π​ 
D) π​   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π​ 
E) π​   $\mathrm { Y } _ { \mathrm { scl } } = \frac { \pi } { 4 }$ -π​

Question 18

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

Accepted Answer

A) 2arccos x 
B) arcsin 2x 
C) arccos (x + 1) 
D) 2arcsin $\frac { x } { 2 }$ 
E) arccos $\frac { x } { 2 }$ 
A) 2arccos x 
B) arcsin 2x 
C) arccos (x + 1) 
D) 2arcsin $\frac { x } { 2 }$ 
E) arccos $\frac { x } { 2 }$

Question 19

Find an algebraic expression that is equivalent to the expression..​ $$\tan \left( \arccos \frac { x } { 6 } \right)$$ ​

Accepted Answer

A)  $\frac { \sqrt { 36 - x ^ { 2 } } } { x }$ 
B)  $\frac { 36 - x ^ { 2 } } { x }$ 
C)  $\frac { \sqrt { 36 + x ^ { 2 } } } { x }$ 
D)  $\frac { \sqrt { 36 + x ^ { 2 } } } { 36 + x ^ { 2 } }$ 
E)  $\frac { \sqrt { 36 - x ^ { 2 } } } { 36 - x ^ { 2 } }$ 
A)  $\frac { \sqrt { 36 - x ^ { 2 } } } { x }$ 
B)  $\frac { 36 - x ^ { 2 } } { x }$ 
C)  $\frac { \sqrt { 36 + x ^ { 2 } } } { x }$ 
D)  $\frac { \sqrt { 36 + x ^ { 2 } } } { 36 + x ^ { 2 } }$ 
E)  $\frac { \sqrt { 36 - x ^ { 2 } } } { 36 - x ^ { 2 } }$

Question 20

Find the value of the expression.Round your result to two decimal places.​ $$\operatorname { arccot } \frac { 7 } { 2 }$$ ​

Accepted Answer

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

Exam 29: Inverse Trigonometric Functions

Evaluate the expression.Round your result to two decimal places.​ arcsin⁡0.45\arcsin 0.45arcsin0.45 ​

Evaluate the expression.Round your result to two decimal places.​ tan⁡−1(−974)\tan ^ { - 1 } \left( - \frac { 97 } { 4 } \right)tan−1(−497​) ​

Evaluate the expression.Round your result to two decimal places.​ arccos⁡(−23)\arccos \left( - \frac { 2 } { 3 } \right)arccos(−32​) ​

Evaluate tan⁡−1(−33)\tan ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)tan−1(−33​​) without using a calculator.

Evaluate the expression.Round your result to two decimal places.​ cos⁡−10.44\cos ^ { - 1 } 0.44cos−10.44 ​

Evaluate the expression.Round your result to two decimal places.​ sin⁡−10.65\sin ^ { - 1 } 0.65sin−10.65 ​

Which of the following can be inserted to make the statement true? arccos⁡(36−x26)=arcsin⁡(),0≤x≤6\arccos \left( \frac { \sqrt { 36 - x ^ { 2 } } } { 6 } \right) = \arcsin ( \quad ) , 0 \leq x \leq 6arccos(636−x2​​)=arcsin(),0≤x≤6

Evaluate the expression.Round your result to two decimal places.​ arctan⁡30\arctan 30arctan30 ​

Evaluate the expression.Round your result to two decimal places.​ arccos⁡0.23\arccos 0.23arccos0.23 ​

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

Evaluate the expression.Round your result to two decimal places.​ arcsin⁡(−0.130)\arcsin ( - 0.130 )arcsin(−0.130) ​

Evaluate the expression.Round your result to two decimal places.​ arcsin⁡23\arcsin \frac { 2 } { 3 }arcsin32​ ​

Evaluate arctan⁡33\arctan \frac { \sqrt { 3 } } { 3 }arctan33​​ without using a calculator.

Write an algebraic expression that is equivalent to tan⁡(arccos⁡3x)\tan ( \arccos 3 x )tan(arccos3x) .

An airplane flies at an altitude of a=6a = 6a=6 miles toward a point directly over an observer.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 arctan⁡[tan⁡(2π5)]\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]arctan[tan(52π​)] .

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

Find an algebraic expression that is equivalent to the expression..​ tan⁡(arccos⁡x6)\tan \left( \arccos \frac { x } { 6 } \right)tan(arccos6x​) ​

Find the value of the expression.Round your result to two decimal places.​ arccot⁡72\operatorname { arccot } \frac { 7 } { 2 }arccot27​ ​

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

Evaluate the expression.Round your result to two decimal places. $\arcsin 0.45$

Evaluate the expression.Round your result to two decimal places. $\tan ^ { - 1 } \left( - \frac { 97 } { 4 } \right)$

Evaluate the expression.Round your result to two decimal places. $\arccos \left( - \frac { 2 } { 3 } \right)$

Evaluate $\tan ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)$ without using a calculator.

Evaluate the expression.Round your result to two decimal places. $\cos ^ { - 1 } 0.44$

Evaluate the expression.Round your result to two decimal places. $\sin ^ { - 1 } 0.65$

Which of the following can be inserted to make the statement true? $\arccos \left( \frac { \sqrt { 36 - x ^ { 2 } } } { 6 } \right) = \arcsin ( \quad ) , 0 \leq x \leq 6$

Evaluate the expression.Round your result to two decimal places. $\arctan 30$

Evaluate the expression.Round your result to two decimal places. $\arccos 0.23$

Evaluate the expression.Round your result to two decimal places. $\arcsin ( - 0.130 )$

Evaluate the expression.Round your result to two decimal places. $\arcsin \frac { 2 } { 3 }$

Evaluate $\arctan \frac { \sqrt { 3 } } { 3 }$ without using a calculator.

Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$ .

An airplane flies at an altitude of $a = 6$ miles toward a point directly over an observer.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 $\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]$ .

Find an algebraic expression that is equivalent to the expression.. $\tan \left( \arccos \frac { x } { 6 } \right)$

Find the value of the expression.Round your result to two decimal places. $\operatorname { arccot } \frac { 7 } { 2 }$