Question 1

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

Question 2

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. ​
Radius r
Central Angle θ
15 centimeters
​66°
​

Accepted Answer

A) s ≈ 19.28 centimeters 
B) s ≈ 15.37 centimeters 
C) s ≈ 17.28 centimeters 
D) s ≈ 5.50 centimeters 
E) s ≈ 15.28 centimeters 
A) s ≈ 19.28 centimeters 
B) s ≈ 15.37 centimeters 
C) s ≈ 17.28 centimeters 
D) s ≈ 5.50 centimeters 
E) s ≈ 15.28 centimeters

Question 3

Find the reference angle   , and   sketch and   in standard position. ​   ​

Accepted Answer

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

Question 4

A point on the end of a tuning fork moves in simple harmonic motion described by ​   ​
Find ω given that the tuning fork for middle C has a frequency 270 of vibrations per second.
​

Accepted Answer

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

Question 5

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places. ​     ​

Accepted Answer

A) 2.00 
B) 11.00 
C) 5.50 
D) 22.00​ 
E) 7.50 
A) 2.00 
B) 11.00 
C) 5.50 
D) 22.00​ 
E) 7.50

Question 6

Find the reference angle   . ​   ​

Accepted Answer

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

Question 7

Convert 185.447° to D°M´S´´ form.

Accepted Answer

A) 185°13´25´´ 
B) 185°22´41´´ 
C) 185°20´37´´ 
D) 185°6´12´´ 
E) 185°26´49´´ 
A) 185°13´25´´ 
B) 185°22´41´´ 
C) 185°20´37´´ 
D) 185°6´12´´ 
E) 185°26´49´´

Question 8

Rewrite   in degree measure.

Accepted Answer

A) 300° 
B) 450° 
C) 600° 
D) 150° 
E) 200° 
A) 300° 
B) 450° 
C) 600° 
D) 150° 
E) 200°

Question 9

Evaluate the trigonometric function using its period as an aid. ​   ​

Accepted Answer

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

Question 10

Find the values of θ in degrees   and radians   without the aid of a calculator. ​sin θ = 1 and csc θ = 1
​
​

Accepted Answer

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

Question 11

Write an equation for the function that is described by the given characteristics. ​
A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of   , and a vertical translation up 2 units.
​

Accepted Answer

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

Question 12

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Csc(-310°)
​

Accepted Answer

A) 2.3054 
B) 3.3054 
C) 1.3054 
D) 4.3054 
E) 1.8054 
A) 2.3054 
B) 3.3054 
C) 1.3054 
D) 4.3054 
E) 1.8054

Question 13

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​
Tan 4.9
​

Accepted Answer

A) -4.9675 
B) -4.8675 
C) -5.1675 
D) -4.7675 
E) -5.2675 
A) -4.9675 
B) -4.8675 
C) -5.1675 
D) -4.7675 
E) -5.2675

Question 14

The length of a shadow of a tree is 120 feet when the angle of elevation of the sun is 33º.Approximate the height of the tree.Approximate the answer to one decimal place. ​

Accepted Answer

A) 77.9 ft 
B) 81.9 ft 
C) 79.9 ft 
D) 78.9 ft 
E) 80.9 ft 
A) 77.9 ft 
B) 81.9 ft 
C) 79.9 ft 
D) 78.9 ft 
E) 80.9 ft

Question 15

Find the angle α between two nonvertical lines   and   .The angle α satisfies the equation ​   ​
Where   and   are slopes of   and   , respectively.
(Assume that   .)
​   : 5x - 4y = 5   : x + y = 1
​
Round your answer to one decimal place.
​

Accepted Answer

A) 83.7º 
B) 84.7º 
C) 85.7º 
D) 86.7º 
E) 87.7º 
A) 83.7º 
B) 84.7º 
C) 85.7º 
D) 86.7º 
E) 87.7º

Question 16

Find the value of the expression.Round your result to two decimal places. ​   ​

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

Question 17

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

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

Question 18

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

Accepted Answer

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

Question 19

Which of the following can be inserted to make the statement true?

Accepted Answer

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

Question 20

A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly.From point A the biologist walks downstream   feet and sights to point C (see figure).From this sighting, it is determined that θ = 54°.How wide is the river? ​   (Round your answer to three decimal places.)
​

Accepted Answer

A) 212.693 
B) 197.693 
C) 207.693 
D) 202.693 
E) 192.693 
A) 212.693 
B) 197.693 
C) 207.693 
D) 202.693 
E) 192.693

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

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. Radius r Central Angle θ 15 centimeters 66°

Find the reference angle , and sketch and in standard position.

A point on the end of a tuning fork moves in simple harmonic motion described by Find ω given that the tuning fork for middle C has a frequency 270 of vibrations per second.

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.

Find the reference angle .

Convert 185.447° to D°M´S´´ form.

Rewrite in degree measure.

Evaluate the trigonometric function using its period as an aid.

Find the values of θ in degrees and radians without the aid of a calculator. sin θ = 1 and csc θ = 1

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units.

Evaluate the trigonometric function.Round your answer to four decimal places. Csc(-310°)

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Tan 4.9

The length of a shadow of a tree is 120 feet when the angle of elevation of the sun is 33º.Approximate the height of the tree.Approximate the answer to one decimal place.

Find the angle α between two nonvertical lines and .The angle α satisfies the equation Where and are slopes of and , respectively. (Assume that .) : 5x - 4y = 5 : x + y = 1 Round your answer to one decimal place.

Find the value of the expression.Round your result to two decimal places.

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

Use the value of the trigonometric function to find .

Which of the following can be inserted to make the statement true?

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

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

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. ​ Radius r Central Angle θ 15 centimeters ​66° ​

Find the reference angle , and sketch and in standard position. ​ ​

A point on the end of a tuning fork moves in simple harmonic motion described by ​ ​ Find ω given that the tuning fork for middle C has a frequency 270 of vibrations per second. ​

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places. ​ ​

Find the reference angle . ​ ​

Convert 185.447° to D°M´S´´ form.

Rewrite in degree measure.

Evaluate the trigonometric function using its period as an aid. ​ ​

Find the values of θ in degrees and radians without the aid of a calculator. ​sin θ = 1 and csc θ = 1 ​ ​

Write an equation for the function that is described by the given characteristics. ​ A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units. ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Csc(-310°) ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​ Tan 4.9 ​

The length of a shadow of a tree is 120 feet when the angle of elevation of the sun is 33º.Approximate the height of the tree.Approximate the answer to one decimal place. ​

Find the angle α between two nonvertical lines and .The angle α satisfies the equation ​ ​ Where and are slopes of and , respectively. (Assume that .) ​ : 5x - 4y = 5 : x + y = 1 ​ Round your answer to one decimal place. ​

Find the value of the expression.Round your result to two decimal places. ​ ​

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

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

Which of the following can be inserted to make the statement true?

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

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

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. Radius r Central Angle θ 15 centimeters 66°

Find the reference angle , and sketch and in standard position.

A point on the end of a tuning fork moves in simple harmonic motion described by Find ω given that the tuning fork for middle C has a frequency 270 of vibrations per second.

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.

Find the reference angle .

Evaluate the trigonometric function using its period as an aid.

Find the values of θ in degrees and radians without the aid of a calculator. sin θ = 1 and csc θ = 1

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units.

Evaluate the trigonometric function.Round your answer to four decimal places. Csc(-310°)

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Tan 4.9

The length of a shadow of a tree is 120 feet when the angle of elevation of the sun is 33º.Approximate the height of the tree.Approximate the answer to one decimal place.

Find the angle α between two nonvertical lines and .The angle α satisfies the equation Where and are slopes of and , respectively. (Assume that .) : 5x - 4y = 5 : x + y = 1 Round your answer to one decimal place.

Find the value of the expression.Round your result to two decimal places.

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

Use the value of the trigonometric function to find .