Question 1

Describe the behavior of the function below as x approaches   . ​   ​

Accepted Answer

A) f → +∞ as x →   . 
B) f → 0 as x →   . 
C) f → 1 as x →   . 
D) f → -∞ as x →   . 
E) f → -1 as x →   . 
A) f → +∞ as x →   . 
B) f → 0 as x →   . 
C) f → 1 as x →   . 
D) f → -∞ as x →   . 
E) f → -1 as x →   .

Question 2

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. ​   ​
A =   , b =   ​

Accepted Answer

A) sin t =   cos t =  
Tan t =   
B) ​sin t =   cos t =  
Tan t =   
C) ​sin t =   cos t =  
Tan t =   
D) sin t =   cos t =  
Tan t =   
E) ​sin t =   cos t =  
Tan t =   
A) sin t =   cos t =  
Tan t =   
B) ​sin t =   cos t =  
Tan t =   
C) ​sin t =   cos t =  
Tan t =   
D) sin t =   cos t =  
Tan t =   
E) ​sin t =   cos t =  
Tan t =

Question 3

Determine the quadrant in which an angle, θ, lies if   .

Accepted Answer

A) 4th quadrant 
B) 2nd quadrant 
C) 1st quadrant 
D) 3rd quadrant 
A) 4th quadrant 
B) 2nd quadrant 
C) 1st quadrant 
D) 3rd quadrant

Question 4

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

Accepted Answer

A)    
B)    
C) 0.4 
D)    
E)    
A)    
B)    
C) 0.4 
D)    
E)

Question 5

Determine the quadrant in which an angle with measure -176°2' lies.

Accepted Answer

A) 3rd quadrant 
B) 2nd quadrant 
C) 1st quadrant 
D) 4th quadrant 
A) 3rd quadrant 
B) 2nd quadrant 
C) 1st quadrant 
D) 4th quadrant

Question 6

A car is traveling along Route 66 at a rate of 55 miles per hour, and the diameter of its wheels are 2.7 feet.Find the number of revolutions per minute the wheels are turning.Round answer to one decimal place.

Accepted Answer

A) 285.3 rpm 
B) 845.3 rpm 
C) 570.6 rpm 
D) 108.1 rpm 
E) 190.2 rpm 
A) 285.3 rpm 
B) 845.3 rpm 
C) 570.6 rpm 
D) 108.1 rpm 
E) 190.2 rpm

Question 7

​Determine the period and amplitude of the following function ​     ​

Accepted Answer

A) ​Period: 16   ; Amplitude: 10 
B) ​Period:   ; Amplitude: 5 
C) ​Period: 5   ; Amplitude: 6 
D) ​Period:   ; Amplitude: 5 
E) ​Period: 8   ; Amplitude: 4 
A) ​Period: 16   ; Amplitude: 10 
B) ​Period:   ; Amplitude: 5 
C) ​Period: 5   ; Amplitude: 6 
D) ​Period:   ; Amplitude: 5 
E) ​Period: 8   ; Amplitude: 4

Question 8

Find the value of given trigonometric function.Round your answer to four decimal places. ​   ​

Accepted Answer

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

Question 9

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which   ​   ​

Accepted Answer

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

Question 10

Using the figure below, if θ = 33° and y = 9, determine the exact value of x.

Accepted Answer

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

Question 11

Find the point   on the unit circle that corresponds to the real number   .Use your results to evaluate cos t. ​

Accepted Answer

A) cos t = 1 
B) cos t = -1 
C)    
D)    
E)    
A) cos t = 1 
B) cos t = -1 
C)    
D)    
E)

Question 12

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​   ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
Select the graph of this velocity function.

Accepted Answer

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

Question 13

Determine the exact value of the   of the quadrant angle   .

Accepted Answer

A)    
B)    
C)    
D) 0 
E) undefined 
A)    
B)    
C)    
D) 0 
E) undefined

Question 14

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

Accepted Answer

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

Question 15

Determine the angle between the diagonal of a cube and its edge, as shown in the figure, where   .Round your answer to one decimal place. ​   ​

Accepted Answer

A) 56.7o 
B) 57.7o 
C) 55.7o 
D) 54.7o 
E) 58.7o ​ 
A) 56.7o 
B) 57.7o 
C) 55.7o 
D) 54.7o 
E) 58.7o ​

Question 16

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. ​   ​   ​

Accepted Answer

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

Question 17

State the period of the function: ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) 1 
A)    
B)    
C)    
D)    
E) 1

Question 18

Using the figure below, if θ = 26° and y = 6, determine the exact value of x.

Accepted Answer

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

Question 19

An airplane, flying at an altitude of 8 miles, is on a flight path that passes directly over an observer (see figure).If   is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when   °.(Round your answers to two decimal place.)
​   ​

Accepted Answer

A) 11.24 mi 
B) 10.24 mi 
C) 9.24 mi 
D) 12.24 mi 
E) 13.24 mi 
A) 11.24 mi 
B) 10.24 mi 
C) 9.24 mi 
D) 12.24 mi 
E) 13.24 mi

Question 20

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0. ​
​

Accepted Answer

A) ​   As x → 0, f(x) → 0. 
B) ​   ​As x → 0, f(x) → 0. 
C) ​   As x → 0, f(x) → 0. 
D) ​   As x → 0, f(x) → 0. 
E) ​   As x → 0, f(x) → 0. 
A) ​   As x → 0, f(x) → 0. 
B) ​   ​As x → 0, f(x) → 0. 
C) ​   As x → 0, f(x) → 0. 
D) ​   As x → 0, f(x) → 0. 
E) ​   As x → 0, f(x) → 0.

Describe the behavior of the function below as x approaches .

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. A = , b =

Determine the quadrant in which an angle, θ, lies if .

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

Determine the quadrant in which an angle with measure -176°2' lies.

A car is traveling along Route 66 at a rate of 55 miles per hour, and the diameter of its wheels are 2.7 feet.Find the number of revolutions per minute the wheels are turning.Round answer to one decimal place.

Determine the period and amplitude of the following function

Find the value of given trigonometric function.Round your answer to four decimal places.

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which

Using the figure below, if θ = 33° and y = 9, determine the exact value of x.

Find the point on the unit circle that corresponds to the real number .Use your results to evaluate cos t.

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

Determine the exact value of the of the quadrant angle .

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

Determine the angle between the diagonal of a cube and its edge, as shown in the figure, where .Round your answer to one decimal place.

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t.

State the period of the function:

Using the figure below, if θ = 26° and y = 6, determine the exact value of x.

An airplane, flying at an altitude of 8 miles, is on a flight path that passes directly over an observer (see figure).If is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when °.(Round your answers to two decimal place.)

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0.

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

Describe the behavior of the function below as x approaches . ​ ​

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. ​ ​ A = , b = ​

Determine the quadrant in which an angle, θ, lies if .

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

Determine the quadrant in which an angle with measure -176°2' lies.

A car is traveling along Route 66 at a rate of 55 miles per hour, and the diameter of its wheels are 2.7 feet.Find the number of revolutions per minute the wheels are turning.Round answer to one decimal place.

​Determine the period and amplitude of the following function ​ ​

Find the value of given trigonometric function.Round your answer to four decimal places. ​ ​

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which ​ ​

Using the figure below, if θ = 33° and y = 9, determine the exact value of x.

Find the point on the unit circle that corresponds to the real number .Use your results to evaluate cos t. ​

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​ , ​ Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

Determine the exact value of the of the quadrant angle .

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

Determine the angle between the diagonal of a cube and its edge, as shown in the figure, where .Round your answer to one decimal place. ​ ​

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. ​ ​ ​

State the period of the function: ​ ​

Using the figure below, if θ = 26° and y = 6, determine the exact value of x.

An airplane, flying at an altitude of 8 miles, is on a flight path that passes directly over an observer (see figure).If is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when °.(Round your answers to two decimal place.) ​ ​

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0. ​ ​

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Describe the behavior of the function below as x approaches .

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t. A = , b =

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

Determine the period and amplitude of the following function

Find the value of given trigonometric function.Round your answer to four decimal places.

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which

Find the point on the unit circle that corresponds to the real number .Use your results to evaluate cos t.

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

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

Determine the angle between the diagonal of a cube and its edge, as shown in the figure, where .Round your answer to one decimal place.

Find the exact values of the three trigonometric functions sine, cosine, tangent of the real number t.

State the period of the function:

An airplane, flying at an altitude of 8 miles, is on a flight path that passes directly over an observer (see figure).If is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when °.(Round your answers to two decimal place.)

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0.