Question 1

Use the value of the trigonometric function to find the   . ​   ​

Accepted Answer

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

Question 2

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 3

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

Accepted Answer

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

Question 4

A plane flying at an altitude of a miles above a radar antenna will pass directly over the radar antenna (see figure).Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna.   . ​
(d is positive as the plane approaches the antenna.)
Write d as a function of x.
​

Accepted Answer

A) d = 8 csc x 
B) d = 8 cot x 
C) d = 8 cos x 
D) d = 8 tan x 
E) d = 8 sin x 
A) d = 8 csc x 
B) d = 8 cot x 
C) d = 8 cos x 
D) d = 8 tan x 
E) d = 8 sin x

Question 5

An airplane flies at an altitude of   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)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​
Sin 11°
​

Accepted Answer

A) 0.4908 
B) 0.1908 
C) 0.5908 
D) 0.2908 
E) 0.6908 
A) 0.4908 
B) 0.1908 
C) 0.5908 
D) 0.2908 
E) 0.6908

Question 7

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 time for one full respiratory cycle.
​

Accepted Answer

A) 7 sec 
B) 9 sec 
C) 3 sec 
D) 8 sec 
E) 6 sec 
A) 7 sec 
B) 9 sec 
C) 3 sec 
D) 8 sec 
E) 6 sec

Question 8

Use a calculator to evaluate   .Round your answer to two decimal places.

Accepted Answer

A) 0.68 
B)    
C) 0.72 
D)    
E) 2.51 
A) 0.68 
B)    
C) 0.72 
D)    
E) 2.51

Question 9

Evaluate (if possible) the sine, cosine, and tangent of the real number. ​   ​

Accepted Answer

A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible 
A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible

Question 10

Determine whether the function below is even, odd, or neither. ​
​   ​

Accepted Answer

A) Even 
B) Odd 
C) Neither 
A) Even 
B) Odd 
C) Neither

Question 11

Describe the behavior of the function below as x approaches 0+. ​   ​

Accepted Answer

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

Question 12

Select the graph of the function.(Include two full periods.) ​
Y = sin 2x
​

Accepted Answer

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

Question 13

If   , find the value of θ in degrees   without the aid of a calculator.

Accepted Answer

A) ​θ = 45° 
B) ​θ = 30° 
C) ​θ = 15° 
D) ​θ = 90° 
E) ​θ = 75° 
A) ​θ = 45° 
B) ​θ = 30° 
C) ​θ = 15° 
D) ​θ = 90° 
E) ​θ = 75°

Question 14

Find the angle   between two nonvertical lines   and   .The angle   satisfies the equation ​   ​
Where   and   are slopes of   and   , respectively.
(Assume that   .)
​
​     ​
Round your answer to one decimal place.
​

Accepted Answer

A) 54.1o 
B) ​53.1o 
C) 55.1o 
D) 52.1o 
E) 56.1o 
A) 54.1o 
B) ​53.1o 
C) 55.1o 
D) 52.1o 
E) 56.1o

Question 15

Using trigonometric identities, determine which of the following is equivalent to the following expression. ​
Tan θ + cot θ   ​

Accepted Answer

A) ​1 
B) ​csc θ sec θ 
C)    ​ θ +   θ 
D) ​cos θ + sec θ 
E) ​sec θ + csc θ 
A) ​1 
B) ​csc θ sec θ 
C)    ​ θ +   θ 
D) ​cos θ + sec θ 
E) ​sec θ + csc θ

Question 16

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

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 17

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound. ​   ​
​

Accepted Answer

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

Question 18

Evaluate (if possible) the sine, cosine, and tangent of the real number. ​   ​

Accepted Answer

A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible 
A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible

Question 19

If   , find the value of θ in degrees   without the aid of a calculator.

Accepted Answer

A) θ = 30° 
B) ​θ = 45° 
C) ​​θ = 90° 
D) ​​θ = 75° 
E) ​​θ = 15° 
A) θ = 30° 
B) ​θ = 45° 
C) ​​θ = 90° 
D) ​​θ = 75° 
E) ​​θ = 15°

Question 20

Use a graphing utility to graph the function below.Be sure to include at least two full periods. y = 4 sin (x - 5π) + 1

Accepted Answer

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

Use the value of the trigonometric function to find the .

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.)

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

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

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Sin 11°

Use a calculator to evaluate .Round your answer to two decimal places.

Evaluate (if possible) the sine, cosine, and tangent of the real number.

Determine whether the function below is even, odd, or neither.

Describe the behavior of the function below as x approaches 0⁺.

Select the graph of the function.(Include two full periods.) Y = sin 2x

If , find the value of θ in degrees without the aid of a calculator.

Find the angle between two nonvertical lines and .The angle satisfies the equation Where and are slopes of and , respectively. (Assume that .) Round your answer to one decimal place.

Using trigonometric identities, determine which of the following is equivalent to the following expression. Tan θ + cot θ

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

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.

Evaluate (if possible) the sine, cosine, and tangent of the real number.

If , find the value of θ in degrees without the aid of a calculator.

Use a graphing utility to graph the function below.Be sure to include at least two full periods. y = 4 sin (x - 5π) + 1

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

Use the value of the trigonometric function to find the . ​ ​

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.)

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

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

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​ Sin 11° ​

Use a calculator to evaluate .Round your answer to two decimal places.

Evaluate (if possible) the sine, cosine, and tangent of the real number. ​ ​

Determine whether the function below is even, odd, or neither. ​ ​ ​

Describe the behavior of the function below as x approaches 0+. ​ ​

Select the graph of the function.(Include two full periods.) ​ Y = sin 2x ​

If , find the value of θ in degrees without the aid of a calculator.

Find the angle between two nonvertical lines and .The angle satisfies the equation ​ ​ Where and are slopes of and , respectively. (Assume that .) ​ ​ ​ Round your answer to one decimal place. ​

Using trigonometric identities, determine which of the following is equivalent to the following expression. ​ Tan θ + cot θ ​

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

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound. ​ ​ ​

Evaluate (if possible) the sine, cosine, and tangent of the real number. ​ ​

If , find the value of θ in degrees without the aid of a calculator.

Use a graphing utility to graph the function below.Be sure to include at least two full periods. y = 4 sin (x - 5π) + 1

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Use the value of the trigonometric function to find the .

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

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

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Sin 11°

Evaluate (if possible) the sine, cosine, and tangent of the real number.

Determine whether the function below is even, odd, or neither.

Describe the behavior of the function below as x approaches 0⁺.

Select the graph of the function.(Include two full periods.) Y = sin 2x

Find the angle between two nonvertical lines and .The angle satisfies the equation Where and are slopes of and , respectively. (Assume that .) Round your answer to one decimal place.

Using trigonometric identities, determine which of the following is equivalent to the following expression. Tan θ + cot θ

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

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.

Evaluate (if possible) the sine, cosine, and tangent of the real number.