Question 1

In each of the four quadrants, the signs of the cosec function and cosine function will be the same.
​

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

A) 33.18 meters 
B) 6.23 meters 
C) 9.98 meters 
D) 16.59 meters 
E) 9.42 meters 
A) 33.18 meters 
B) 6.23 meters 
C) 9.98 meters 
D) 16.59 meters 
E) 9.42 meters

Question 3

Find the exact values of the six trigonometric functions of the angle θ for each of the two triangles.     ​

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 4

A carousel with a 60-foot diameter makes 2 revolutions per minute.Find the angular speed of the carousel in radians per minute.Round your answer to two decimal places. ​

Accepted Answer

A) 2 rpm ≈ 61.85 radians per minute 
B) 2 rpm ≈ 12.57 radians per minute 
C) 2 rpm ≈ 18.85 radians per minute 
D) 2 rpm ≈ 6.28 radians per minute 
E) 2 rpm ≈ 58.23 radians per minute 
A) 2 rpm ≈ 61.85 radians per minute 
B) 2 rpm ≈ 12.57 radians per minute 
C) 2 rpm ≈ 18.85 radians per minute 
D) 2 rpm ≈ 6.28 radians per minute 
E) 2 rpm ≈ 58.23 radians per minute

Question 5

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

Accepted Answer

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

Question 6

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

Accepted Answer

A) S = 9.42 meters 
B) S = 12.57 meters 
C) S = 18.85 meters 
D) S = 6.28 meters 
E) S = 7.54 meters 
A) S = 9.42 meters 
B) S = 12.57 meters 
C) S = 18.85 meters 
D) S = 6.28 meters 
E) S = 7.54 meters

Question 7

Consider the functions given by ​   on the interval (0, π).
Describe the behavior of each of the functions as x approaches π.
​

Accepted Answer

A) f approaches 2 and g approaches +∞. 
B) f approaches 0 and g approaches +∞. 
C) f approaches +∞ and g approaches 0. 
D) f approaches 0 and g approaches   . 
E) f approaches 2 and g approaches   . 
A) f approaches 2 and g approaches +∞. 
B) f approaches 0 and g approaches +∞. 
C) f approaches +∞ and g approaches 0. 
D) f approaches 0 and g approaches   . 
E) f approaches 2 and g approaches   .

Question 8

Find angle 45° in radian measure as a multiple of π. ​

Accepted Answer

A)    
B)    
C) 4π 
D)    
E)    
A)    
B)    
C) 4π 
D)    
E)

Question 9

Find angle   in degree measure. ​

Accepted Answer

A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245° 
A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245°

Question 10

Use the properties of inverse trigonometric functions to evaluate   .

Accepted Answer

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

Question 11

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

Accepted Answer

A) 1.1998 and 0.4463 
B) 1.2998 and 0.5463 
C) 1.1498 and 0.3963 
D) 1.0998 and 0.3463 
E) 1.2498 and 0.4963 
A) 1.1998 and 0.4463 
B) 1.2998 and 0.5463 
C) 1.1498 and 0.3963 
D) 1.0998 and 0.3463 
E) 1.2498 and 0.4963

Question 12

Find the exact value of csc θ, using the triangle shown in the figure below, if   and   .

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A)    0.3142 
B)    0.6142 
C)    - 0.4142 
D)    0.4142 
E)    0.5142 
A)    0.3142 
B)    0.6142 
C)    - 0.4142 
D)    0.4142 
E)    0.5142

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

For the simple harmonic motion described by the trigonometric function, find the maximumvalue of d when . ​   Round your answer to nearest whole number.
​

Accepted Answer

A) 1 
B) 10 
C) 6 
D) 5 
E) 0 
A) 1 
B) 10 
C) 6 
D) 5 
E) 0

Question 18

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of 4π, an amplitude of 4, a left phase shift of   , and a vertical translation down 5 units.
​

Accepted Answer

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

Question 19

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction 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 answer to two decimal places. ​   ​
​

Accepted Answer

A) 0.89 cm 
B) 0.59 cm 
C) 0.99 cm 
D) 1.09 cm 
E) 0.79 cm 
A) 0.89 cm 
B) 0.59 cm 
C) 0.99 cm 
D) 1.09 cm 
E) 0.79 cm

Question 20

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​
Sec 0.21
​

Accepted Answer

A) 1.5225 
B) 1.1225 
C) 1.4225 
D) 1.0225 
E) 1.3225 
A) 1.5225 
B) 1.1225 
C) 1.4225 
D) 1.0225 
E) 1.3225

In each of the four quadrants, the signs of the cosec function and cosine function will be the same.

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

Find the exact values of the six trigonometric functions of the angle θ for each of the two triangles.

A carousel with a 60-foot diameter makes 2 revolutions per minute.Find the angular speed of the carousel in radians per minute.Round your answer to two decimal places.

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

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

Consider the functions given by on the interval (0, π). Describe the behavior of each of the functions as x approaches π.

Find angle 45° in radian measure as a multiple of π.

Find angle in degree measure.

Use the properties of inverse trigonometric functions to evaluate .

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

Find the exact value of csc θ, using the triangle shown in the figure below, if and .

Use the value of the trigonometric function to find .

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

Use the value of the trigonometric function to find .

Use the value of the trigonometric function to find .

For the simple harmonic motion described by the trigonometric function, find the maximumvalue of d when . Round your answer to nearest whole number.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units.

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction 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 answer to two decimal places.

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Sec 0.21

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

In each of the four quadrants, the signs of the cosec function and cosine function will be the same. ​

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

Find the exact values of the six trigonometric functions of the angle θ for each of the two triangles. ​

A carousel with a 60-foot diameter makes 2 revolutions per minute.Find the angular speed of the carousel in radians per minute.Round your answer to two decimal places. ​

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

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

Consider the functions given by ​ on the interval (0, π). Describe the behavior of each of the functions as x approaches π. ​

Find angle 45° in radian measure as a multiple of π. ​

Find angle in degree measure. ​

Use the properties of inverse trigonometric functions to evaluate .

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

Find the exact value of csc θ, using the triangle shown in the figure below, if and .

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

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

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

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

For the simple harmonic motion described by the trigonometric function, find the maximumvalue of d when . ​ Round your answer to nearest whole number. ​

Write an equation for the function that is described by the given characteristics. ​ A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units. ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​ Sec 0.21 ​

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

In each of the four quadrants, the signs of the cosec function and cosine function will be the same.

Find the exact values of the six trigonometric functions of the angle θ for each of the two triangles.

A carousel with a 60-foot diameter makes 2 revolutions per minute.Find the angular speed of the carousel in radians per minute.Round your answer to two decimal places.

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

Consider the functions given by on the interval (0, π). Describe the behavior of each of the functions as x approaches π.

Find angle 45° in radian measure as a multiple of π.

Find angle in degree measure.

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

Use the value of the trigonometric function to find .

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

Use the value of the trigonometric function to find .

Use the value of the trigonometric function to find .

For the simple harmonic motion described by the trigonometric function, find the maximumvalue of d when . Round your answer to nearest whole number.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units.

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) Sec 0.21