Question 1

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 2

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

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 3

If the sides of a rectangular solid are as shown, and   , determine the angle, θ, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

Accepted Answer

A) 21.91o 
B) 24.09o 
C) 17.21o 
D) 26.28o 
E) 19.86o 
A) 21.91o 
B) 24.09o 
C) 17.21o 
D) 26.28o 
E) 19.86o

Question 4

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

Accepted Answer

A) ​Period: 10   ; Amplitude: 6 
B) ​Period:   ; Amplitude: 3 
C) ​Period: 8   ; Amplitude: 4 
D) ​Period:   ; Amplitude: 3 
E) ​Period: 5   ; Amplitude: 2 
A) ​Period: 10   ; Amplitude: 6 
B) ​Period:   ; Amplitude: 3 
C) ​Period: 8   ; Amplitude: 4 
D) ​Period:   ; Amplitude: 3 
E) ​Period: 5   ; Amplitude: 2

Question 5

Use a graphing utility to select the graph of the function: ​   ​

Accepted Answer

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

Question 6

Use a calculator to evaluate tan 68°23'.Round your answer to four decimal places.

Accepted Answer

A) 2.5236 
B) 2.5040 
C) -1.2222 
D) -0.8980 
E) 0.7269 
A) 2.5236 
B) 2.5040 
C) -1.2222 
D) -0.8980 
E) 0.7269

Question 7

Use the properties of inverse trigonometric functions to evaluate   .

Accepted Answer

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

Question 8

Select a right triangle corresponding to the trigonometric function of the acute angle θ.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. ​
Tan θ =   ​
​
Sin θ =   csc θ =   cos θ =   sec θ =   tan θ =   cot θ =   ​

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 9

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

Accepted Answer

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

Question 10

Select the graph of the function.(Include two full periods.) ​   ​

Accepted Answer

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

Question 11

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 12

Given the figure below, determine the value of   . ​   ​

Accepted Answer

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

Question 13

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

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

Question 14

Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​   ​
Where   ​

Accepted Answer

A) sin θ =   cos θ =  
Tan θ =   
B) sin θ =   cos θ =  
Tan θ =   
C) sin θ =   cos θ =  
Tan θ =   
D) sin θ =   cos θ =  
Tan θ =   
E) sin θ =   cos θ =  
Tan θ =   
A) sin θ =   cos θ =  
Tan θ =   
B) sin θ =   cos θ =  
Tan θ =   
C) sin θ =   cos θ =  
Tan θ =   
D) sin θ =   cos θ =  
Tan θ =   
E) sin θ =   cos θ =  
Tan θ =

Question 15

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

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 16

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by ​   ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
​
Find the number of cycles per minute.
​

Accepted Answer

A) 14 cycles/min 
B) 11 cycles/min 
C) 10 cycles/min 
D) 15 cycles/min 
E) 12 cycles/min 
A) 14 cycles/min 
B) 11 cycles/min 
C) 10 cycles/min 
D) 15 cycles/min 
E) 12 cycles/min

Question 17

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​   ​

Accepted Answer

A) sin θ =   cos θ =  
Tan θ =   
B) sin θ =   cos θ =  
Tan θ =   
C) sin θ =   cos θ =  
Tan θ =   
D) sin θ =   cos θ =  
Tan θ =   
E) sin θ =   cos θ =  
Tan θ =   
A) sin θ =   cos θ =  
Tan θ =   
B) sin θ =   cos θ =  
Tan θ =   
C) sin θ =   cos θ =  
Tan θ =   
D) sin θ =   cos θ =  
Tan θ =   
E) sin θ =   cos θ =  
Tan θ =

Question 18

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

Accepted Answer

A) 38.3o 
B) 36.3o 
C) 39.3o 
D) 35.3o 
E) 37.3o 
A) 38.3o 
B) 36.3o 
C) 39.3o 
D) 35.3o 
E) 37.3o

Question 19

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

Accepted Answer

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

Question 20

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. ​   ​   ​

Accepted Answer

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

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

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

If the sides of a rectangular solid are as shown, and , determine the angle, θ, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

Determine the period and amplitude of the following function

Use a graphing utility to select the graph of the function:

Use a calculator to evaluate tan 68°23'.Round your answer to four decimal places.

Use the properties of inverse trigonometric functions to evaluate .

Select a right triangle corresponding to the trigonometric function of the acute angle θ.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. Tan θ = Sin θ = csc θ = cos θ = sec θ = tan θ = cot θ =

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

Select the graph of the function.(Include two full periods.)

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

Given the figure below, determine the value of .

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

Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. Where

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

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ.

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

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

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

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

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

If the sides of a rectangular solid are as shown, and , determine the angle, θ, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

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

Use a graphing utility to select the graph of the function: ​ ​

Use a calculator to evaluate tan 68°23'.Round your answer to four decimal places.

Use the properties of inverse trigonometric functions to evaluate .

Select a right triangle corresponding to the trigonometric function of the acute angle θ.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. ​ Tan θ = ​ ​ Sin θ = csc θ = cos θ = sec θ = tan θ = cot θ = ​

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

Select the graph of the function.(Include two full periods.) ​ ​

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

Given the figure below, determine the value of . ​ ​

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

Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​ ​ Where ​

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

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​ ​

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

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

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. ​ ​ ​

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

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

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

Determine the period and amplitude of the following function

Use a graphing utility to select the graph of the function:

Select a right triangle corresponding to the trigonometric function of the acute angle θ.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. Tan θ = Sin θ = csc θ = cos θ = sec θ = tan θ = cot θ =

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

Select the graph of the function.(Include two full periods.)

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

Given the figure below, determine the value of .

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

Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. Where

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

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ.

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

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

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.