Question 1

Find the values of θ in degrees   and radians   without the aid of a calculator. cos θ = 0 and tan θ = Not defined
​
​

Accepted Answer

A) 90° =   
B) ​60° =   
C) ​0° = 0 
D) ​30° =   
E) ​45° =   
A) 90° =   
B) ​60° =   
C) ​0° = 0 
D) ​30° =   
E) ​45° =

Question 2

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

Question 3

Write an algebraic expression that is equivalent to   .

Accepted Answer

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

Question 4

The terminal side of θ lies on the line   in the fourth quadrant.Find the exact value of   .

Accepted Answer

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

Question 5

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Cot 3.35
​

Accepted Answer

A) 7.7286 
B) 5.7286 
C) 5.2286 
D) 6.7286 
E) 4.7286 
A) 7.7286 
B) 5.7286 
C) 5.2286 
D) 6.7286 
E) 4.7286

Question 6

Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)   ​

Accepted Answer

A) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
B) sin θ =   ​ csc θ =   ​
Cos θ =   ​
Sec θ =   ​
Tan θ =   ​
Cot θ =   ​
​ 
C) sin θ =   ​ csc θ =   ​
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
D) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
E) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
A) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
B) sin θ =   ​ csc θ =   ​
Cos θ =   ​
Sec θ =   ​
Tan θ =   ​
Cot θ =   ​
​ 
C) sin θ =   ​ csc θ =   ​
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
D) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​ 
E) sin θ =   csc θ =  
Cos θ =  
Sec θ =  
Tan θ =  
Cot θ =  
​

Question 7

Determine the exact value of   when   and   < 0.

Accepted Answer

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

Question 8

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by ​   ,
​
Where t is the time (in days), with t = 1 corresponding to January 1.
What is the average daily fuel consumption?
​

Accepted Answer

A) 365 gal. 
B) 21.6 gal. 
C) 30 gal. 
D) 10.2 gal. 
E) 30.4 gal. 
A) 365 gal. 
B) 21.6 gal. 
C) 30 gal. 
D) 10.2 gal. 
E) 30.4 gal.

Question 9

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

Accepted Answer

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

Question 10

Find the altitude of the isosceles triangle shown below if   and   .Round your answer to two decimal places.

Accepted Answer

A) 5.12 centimeters 
B) 6.25 centimeters 
C) 3.13 centimeters 
D) 2.46 centimeters 
E) 1.38 centimeters 
A) 5.12 centimeters 
B) 6.25 centimeters 
C) 3.13 centimeters 
D) 2.46 centimeters 
E) 1.38 centimeters

Question 11

State the period of the function: ​   ​

Accepted Answer

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

Question 12

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. ​   ​

Accepted Answer

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

Question 13

Evaluate the trigonometric function.Round your answer to four decimal places. ​   ​

Accepted Answer

A) 2.2321 
B) 1.7321 
C) 2.7321 
D) 3.7321 
E) 4.7321 
A) 2.2321 
B) 1.7321 
C) 2.7321 
D) 3.7321 
E) 4.7321

Question 14

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

Accepted Answer

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

Question 15

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

Accepted Answer

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

Question 16

If θ is an acute angle and   , determine sin θ.

Accepted Answer

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

Question 17

Convert the angle measure from degrees to radians.Round to three decimal places. ​
-206.4°
​

Accepted Answer

A) -206.4° ≈ -3.902 radians 
B) -206.4° ≈ -3.502 radians 
C) -206.4° ≈ -3.602 radians 
D) -206.4° ≈ 3.502 radians 
E) -206.4° ≈ 3.602 radians 
A) -206.4° ≈ -3.902 radians 
B) -206.4° ≈ -3.502 radians 
C) -206.4° ≈ -3.602 radians 
D) -206.4° ≈ 3.502 radians 
E) -206.4° ≈ 3.602 radians

Question 18

Evaluate each function.Round your answers to four decimal places. ​   and   ​

Accepted Answer

A) 4.7046 and 0.2126 
B) 4.7546 and 0.2626 
C) 4.8546 and 0.3626 
D) 4.8046 and 0.3126 
E) 4.9046 and 0.4126 
A) 4.7046 and 0.2126 
B) 4.7546 and 0.2626 
C) 4.8546 and 0.3626 
D) 4.8046 and 0.3126 
E) 4.9046 and 0.4126

Question 19

The displacement from equilibrium of an oscillating weight suspended by a spring is given by ​   , where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when   .(Round your answers to two decimal places.)
​   ​
​

Accepted Answer

A) 1.76 cm 
B) 1.66 cm 
C) 1.46 cm 
D) 1.86 cm 
E) 1.96 cm 
A) 1.76 cm 
B) 1.66 cm 
C) 1.46 cm 
D) 1.86 cm 
E) 1.96 cm

Question 20

Find the quadrant in which the given angle lies. ​
116°
​

Accepted Answer

A) Quadrant I 
B) Quadrant IV 
C) Quadrant III 
D) Quadrant II 
E) None of the above 
A) Quadrant I 
B) Quadrant IV 
C) Quadrant III 
D) Quadrant II 
E) None of the above

Find the values of θ in degrees and radians without the aid of a calculator. cos θ = 0 and tan θ = Not defined

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

Write an algebraic expression that is equivalent to .

The terminal side of θ lies on the line in the fourth quadrant.Find the exact value of .

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 3.35

Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)

Determine the exact value of when and < 0.

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by , Where t is the time (in days), with t = 1 corresponding to January 1. What is the average daily fuel consumption?

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

Find the altitude of the isosceles triangle shown below if and .Round your answer to two decimal places.

State the period of the function:

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.

Evaluate the trigonometric function.Round your answer to four decimal places.

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

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

If θ is an acute angle and , determine sin θ.

Convert the angle measure from degrees to radians.Round to three decimal places. -206.4°

Evaluate each function.Round your answers to four decimal places. and

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when .(Round your answers to two decimal places.)

Find the quadrant in which the given angle lies. 116°

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

Find the values of θ in degrees and radians without the aid of a calculator. cos θ = 0 and tan θ = Not defined ​ ​

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

Write an algebraic expression that is equivalent to .

The terminal side of θ lies on the line in the fourth quadrant.Find the exact value of .

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Cot 3.35 ​

Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) ​

Determine the exact value of when and < 0.

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by ​ , ​ Where t is the time (in days), with t = 1 corresponding to January 1. What is the average daily fuel consumption? ​

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

Find the altitude of the isosceles triangle shown below if and .Round your answer to two decimal places.

State the period of the function: ​ ​

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. ​ ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ ​

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

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

If θ is an acute angle and , determine sin θ.

Convert the angle measure from degrees to radians.Round to three decimal places. ​ -206.4° ​

Evaluate each function.Round your answers to four decimal places. ​ and ​

The displacement from equilibrium of an oscillating weight suspended by a spring is given by ​ , where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when .(Round your answers to two decimal places.) ​ ​ ​

Find the quadrant in which the given angle lies. ​ 116° ​

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find the values of θ in degrees and radians without the aid of a calculator. cos θ = 0 and tan θ = Not defined

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 3.35

Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by , Where t is the time (in days), with t = 1 corresponding to January 1. What is the average daily fuel consumption?

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

State the period of the function:

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.

Evaluate the trigonometric function.Round your answer to four decimal places.

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

Convert the angle measure from degrees to radians.Round to three decimal places. -206.4°

Evaluate each function.Round your answers to four decimal places. and

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when .(Round your answers to two decimal places.)

Find the quadrant in which the given angle lies. 116°