We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Angle Applications

Study concepts, example questions & explanations for Trigonometry

Create An Account

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Angle Applications

What is the formula for angular velocity?

Possible Answers:

$\omega = \frac{r}{l_A}$

$\omega = \frac{\theta}{l_A}$

$\omega = \frac{\theta}{t}$

$\omega = \frac{\theta}{r}$

Correct answer:

$\omega = \frac{\theta}{t}$

Explanation:

Angular velocity is a measure of the time it takes to travel over a certain arc that is formed by a central angle. $\omega$ is usually used to represent the angular velocity, $\theta$ is the measure of the central angle, and is the time it takes to travel from point A to B. This formula looks similar to the measure of an arc, $\theta = \frac{r}{l_A}$ , but we are considering the velocity in terms of the measure of the angle over the amount of time it took to cover that distance.

Report an Error

Example Question #1 : Angle Applications

What is the angular velocity of an angle whose measure is $\frac{5\pi}{4}$ when it took a point 6 seconds to rotate through the angle.

Possible Answers:

$\omega = \frac{10\pi}{24}$ radians/seconds

$\omega = \frac{5\pi}{24}$ radians/seconds

$\omega = 5\pi$ radians/seconds

$\omega = \frac{5\pi}{20}$ radians/seconds

Correct answer:

$\omega = \frac{5\pi}{24}$ radians/seconds

Explanation:

We have enough information to plug into the angular velocity formula to solve this problem. $\theta = \frac{5\pi}{4}$ and t = 6 seconds.

$\omega = \frac{\theta}{t}$

$\omega = (\frac{5\pi}{4})(\frac{1}{6})$

$\omega = \frac{5\pi}{24}$

So our answer is $\omega = \frac{5\pi}{24}$ radians/seconds

Report an Error

Example Question #3 : Angle Applications

True or False: The angular velocity is a measure of an angle of rotation over time.

Possible Answers:

False

True

Correct answer:

True

Explanation:

consider the figure below. Think of line A being connected to a hinge where $\theta$ is. We are measuring the amount of time it takes for line A to rotate and align with line B. This is a measure of angle rotation over time.

Report an Error

Example Question #4 : Angle Applications

What is the angular velocity of an angle whose measure is $\frac{\pi}{3}$ when it took a point 10 seconds to rotate through the angle.

Possible Answers:

$\omega = \frac{8\pi}{30}$ radians/seconds

$\omega = 10\pi$ radians/seconds

$\omega = \frac{\pi}{30}$ radians/seconds

$\omega = 30\pi$ radians/seconds

Correct answer:

$\omega = \frac{\pi}{30}$ radians/seconds

Explanation:

We have enough information to plug into the angular velocity formula to solve this problem. $\theta = \frac{\pi}{3}$ and t = 10 seconds.

$\omega = \frac{\theta}{t}$

$\omega = (\frac{\pi}{3})(\frac{1}{10})$

$\omega = \frac{\pi}{30}$

And so our answer is $\omega = \frac{\pi}{30}$ radians/seconds.

Report an Error

Example Question #5 : Angular Velocity

If you are walking around a circular track and your angular velocity through the angle $\theta = \frac{\pi}{6}$ is $\omega = \frac{\pi}{12}$ , how long would it take you to complete a full rotation?

Possible Answers:

22 seconds

24 seconds

12 seconds

2 seconds

Correct answer:

24 seconds

Explanation:

This is simply solving for an unknown. Here our unknown is time, . So we know that it takes you have an angular velocity of $\omega = \frac{\pi}{12}$ through the angle $\theta = \frac{\pi}{6}$ . Assuming that your angular velocity is consistent, we will be able to solve for . First we must manipulate our original angular velocity formula to solve for .

$\omega = \frac{\theta}{t}$

$t = \frac{\theta}{\omega}$

Now we will plug in our known value for $\omega$ and the angle of a full rotation. The angle of a full rotation is simply that of a full circle, $2\pi$ .

$t = \frac{\theta}{\omega}$

$t = \frac{2\pi}{\frac{\pi}{12}}$

$t = 2\pi (\frac{12}{\pi})$

t = 24

So it takes you 24 seconds to complete a full rotation

Report an Error

Example Question #6 : Angular Velocity

You are on a carousel and have completed one full rotation in 15 seconds. What is your angular velocity?

Possible Answers:

$\omega = 15$ radians/seconds

$\omega = \frac{7\pi}{13}$ radians/seconds

$\omega = \frac{2\pi}{15}$ radians/seconds

$\omega = 2\pi$ radians/seconds

Correct answer:

$\omega = \frac{2\pi}{15}$ radians/seconds

Explanation:

Even though we are not directly given an angle measurement, we are told the time it takes to complete one full rotation. One rotation is the same as the angle of an entire circle, $2\pi$ . Now we have enough information to plug into the angular velocity formula to solve this problem.

$\omega = \frac{\theta}{t}$

$\omega = \frac{2\pi}{15}$

So the angular velocity is $\omega = \frac{2\pi}{15}$ radians/seconds

Report an Error

Example Question #2 : Angle Applications

A wheel is making one full rotation with an angular velocity of $\frac{5\pi }{2}$ radians/seconds. How long will it take the wheel to make 10 full rotations?

Possible Answers:

20 seconds

8 seconds

24 seconds

1 second

Correct answer:

8 seconds

Explanation:

We know that the angular velocity to complete a full rotation (rotate through an angle of $2\pi$ ) is $\frac{5\pi}{2}$ radians/seconds. The angle of 10 full rotations will be 10 rotations through the angle $2\pi$ , so we multiply these two quantities.

$10 *2\pi = 20\pi$

And this will be our $\theta$ . Now we must manipulate our angular velocity formula to solve for .

$\omega = \frac{\theta}{t}$

$t = \frac{\theta}{\omega}$

Now we can plug in our $\theta$ for the 10 rotations and our angular velocity.

$t = \frac{\theta}{\omega}$

$t = \frac{20\pi}{\frac{5\pi}{2}}$

$t = 20\pi \frac{2}{5\pi}$

t = 8

And so it will take 8 seconds to make 10 rotations.

Report an Error

Example Question #1 : Angular Velocity

If it takes you 3 seconds to rotate through an angle with an angular velocity of $\frac{8\pi}{9}$ , what is the measure of the angle you are rotating through?

Possible Answers:

$\theta = \frac{\pi}{3}$

$\theta = \frac{8\pi}{9}$

$3\pi$

$\theta = \frac{8\pi}{3}$

Correct answer:

$\theta = \frac{8\pi}{3}$

Explanation:

We are able to use the angular velocity formula and solve for the unknown $\theta$ .

$\omega = \frac{\theta}{t}$

$\omega t = \theta$

$\frac{8\pi}{9} (3) = \theta$ (making it so we are solving for $\theta$ )

$\frac{24\pi}{9} = \theta$

$\frac{8\pi}{3} = \theta$

Report an Error

Example Question #1 : Area Of A Sector

Which of the following is the definition for a sector of a circle?

Possible Answers:

A section of a circle which is enclosed by a chord and the chord’s arc

Any section of a circle

A section of a circle which is enclosed by two radii joined at the center of the circle and the arc between the two radii

Any section of a circle that is triangular in shape

Correct answer:

A section of a circle which is enclosed by two radii joined at the center of the circle and the arc between the two radii

Explanation:

Below is an illustration of a sector of a circle. A sector is the area of a circle which has been enclosed by two radii and the arc between them. A sector is not to be confused with a segment of a circle. A segment is when the area enclosed by the chord of a circle and the arc of the chord.

Report an Error

Example Question #2 : Area Of A Sector

Which of the following is the formula for the area of a sector?

Possible Answers:

$A = \theta \pi r^2$

$A = \frac{\theta\pi}{2} r^2$

$A = \frac{\theta}{2} r^2$

$A = 2\theta r^2$

Correct answer:

$A = \frac{\theta}{2} r^2$

Explanation:

When thinking about how to derive the formula for a sector, we must consider the angle of an entire circle. The angle of an entire circle, 360 degrees, is $2\pi$ and we know the area of a circle is $\pi r^2$ .

When considering a sector, this is only a portion of the entire circle, so it is a particular $\theta$ out of the entire $2\pi$ . We can plug this into our area for a circle and it will simplify to the area of a sector.

$\frac{\theta}{2\pi}\pi r^2$

$\frac{\theta}{2} r^2$

Report an Error

View Trigonometry Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

View Trigonometry Tutors

Vandana
Certified Tutor

Jawaharlal Nehru Technological University, Bachelor of Technology, Civil Engineering. Florida International University, Maste...

View Trigonometry Tutors

Vicky
Certified Tutor

Clemson University, Doctor of Science, Civil Engineering.

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

ACT Courses & Classes in Chicago, ISEE Courses & Classes in Houston, ACT Courses & Classes in Boston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Miami, SAT Courses & Classes in Boston, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Washington DC, SSAT Test Prep in New York City, GMAT Test Prep in New York City, GMAT Test Prep in Seattle, MCAT Test Prep in Miami, SAT Test Prep in Denver, MCAT Test Prep in Los Angeles, LSAT Test Prep in Seattle, ISEE Test Prep in Philadelphia, SSAT Test Prep in Dallas Fort Worth

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Trigonometry : Angle Applications

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Angle Applications

Example Question #1 : Angle Applications

Example Question #3 : Angle Applications

Example Question #4 : Angle Applications

Example Question #5 : Angular Velocity

Example Question #6 : Angular Velocity

Example Question #2 : Angle Applications

Example Question #1 : Angular Velocity

Example Question #1 : Area Of A Sector

Example Question #2 : Area Of A Sector

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: