We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Angle Measures in Degrees and Radians

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Angle Measures In Degrees And Radians

Convert $240^{\circ}$ $\displaystyle 240^{\circ}$ to radians.

Possible Answers:

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

$\frac{43200}{\pi }$ $\displaystyle \frac{43200}{\pi }$

$\frac{4}{3}\pi$ $\displaystyle \frac{4}{3}\pi$

$\frac{3}{4}\pi$ $\displaystyle \frac{3}{4}\pi$

Correct answer:

$\frac{4}{3}\pi$ $\displaystyle \frac{4}{3}\pi$

Explanation:

In order to solve this problem, we must know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$ $\displaystyle \text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

with this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}}) \times 240^{\circ}=\frac{4}{3}\pi$ $\displaystyle (\frac{\pi }{180^{\circ}}) \times 240^{\circ}=\frac{4}{3}\pi$

Report an Error

Example Question #2 : Angle Measures In Degrees And Radians

Convert $330^{\circ}$ $\displaystyle 330^{\circ}$ to radians.

Possible Answers:

$\frac{11}{6}\pi$ $\displaystyle \frac{11}{6}\pi$

$\frac{59400}{\pi }$ $\displaystyle \frac{59400}{\pi }$

$\frac{6}{11}\pi$ $\displaystyle \frac{6}{11}\pi$

$\frac{11}{6}$ $\displaystyle \frac{11}{6}$

Correct answer:

$\frac{11}{6}\pi$ $\displaystyle \frac{11}{6}\pi$

Explanation:

In order to solve this problem, we need to know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$ $\displaystyle \text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

using this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}})\times330^{\circ}= \frac{11}{6}\pi$ $\displaystyle (\frac{\pi }{180^{\circ}})\times330^{\circ}= \frac{11}{6}\pi$

Report an Error

Example Question #3 : Angle Measures In Degrees And Radians

Convert $\frac{5}{6}\pi$ $\displaystyle \frac{5}{6}\pi$ to degrees.

Possible Answers:

$216^{\circ}$ $\displaystyle 216^{\circ}$

$150\pi$ $\displaystyle 150\pi$

$\frac{\pi }{216}$ $\displaystyle \frac{\pi }{216}$

$150^{\circ}$ $\displaystyle 150^{\circ}$

Correct answer:

$150^{\circ}$ $\displaystyle 150^{\circ}$

Explanation:

In order to solve this problem, we need to know that

$\text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$ $\displaystyle \text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$

using this formula, we can find our answer:

$(\frac{180^{\circ}}{\pi }) \times \frac{5\pi }{6}= 150^{\circ}$ $\displaystyle (\frac{180^{\circ}}{\pi }) \times \frac{5\pi }{6}= 150^{\circ}$

Report an Error

Example Question #4 : Angle Measures In Degrees And Radians

Convert $180^{\circ}$ $\displaystyle 180^{\circ}$ to radians.

Possible Answers:

$3\pi$ $\displaystyle 3\pi$

$\pi$ $\displaystyle \pi$

$180\pi$ $\displaystyle 180\pi$

$\frac{1}{\pi }$ $\displaystyle \frac{1}{\pi }$

$2\pi$ $\displaystyle 2\pi$

Correct answer:

$\pi$ $\displaystyle \pi$

Explanation:

To solve this problem, we need to know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$ $\displaystyle \text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

we can arrive to our answer by using this formula:

$(\frac{\pi }{180^{\circ}})\times 180^{\circ}=\pi$ $\displaystyle (\frac{\pi }{180^{\circ}})\times 180^{\circ}=\pi$

Report an Error

Example Question #5 : Angle Measures In Degrees And Radians

Convert $\frac{3\pi }{2}$ $\displaystyle \frac{3\pi }{2}$ to degrees.

Possible Answers:

$270^{\circ}$ $\displaystyle 270^{\circ}$

$120\pi$ $\displaystyle 120\pi$

$270\pi$ $\displaystyle 270\pi$

$120^{\circ}$ $\displaystyle 120^{\circ}$

$45^\circ$ $\displaystyle 45^\circ$

Correct answer:

$270^{\circ}$ $\displaystyle 270^{\circ}$

Explanation:

In order to solve this problem, we need to know that

$\text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$ $\displaystyle \text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$

we can arrive to our answer by using this formula:

$(\frac{180^{\circ}}{\pi })\times (\frac{3\pi }{2})=270^{\circ}$ $\displaystyle (\frac{180^{\circ}}{\pi })\times (\frac{3\pi }{2})=270^{\circ}$

Report an Error

Example Question #6 : Convert Between Degrees And Radians

Find $90^{\circ}$ $\displaystyle 90^{\circ}$ expressed as radians.

Possible Answers:

$\pi$ $\displaystyle \pi$

$\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$

$\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$

$\frac{\pi}{4}$ $\displaystyle \frac{\pi}{4}$

Correct answer:

$\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$

Explanation:

To convert from degrees into radians,

multiply the angle in degrees by $\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

$90\cdot \frac{\pi}{180}=\frac{\pi}{2}$ $\displaystyle 90\cdot \frac{\pi}{180}=\frac{\pi}{2}$

Report an Error

Example Question #7 : Convert Between Degrees And Radians

Convert the following to degrees:

$\frac{7\pi}{6}$ $\displaystyle \frac{7\pi}{6}$

Possible Answers:

$225^\circ$ $\displaystyle 225^\circ$

$180^\circ$ $\displaystyle 180^\circ$

$210^\circ$ $\displaystyle 210^\circ$

$270^\circ$ $\displaystyle 270^\circ$

Correct answer:

$210^\circ$ $\displaystyle 210^\circ$

Explanation:

To convert, multiply by the conversion factor $\frac{180}{\pi}$ $\displaystyle \frac{180}{\pi}$.

$\frac{7\pi}{6}*\frac{180}{\pi}=7*30=210$ $\displaystyle \frac{7\pi}{6}*\frac{180}{\pi}=7*30=210$

Report an Error

Example Question #8 : Convert Between Degrees And Radians

Convert 1140 $\displaystyle 1140$ degrees into radians.

Possible Answers:

$\frac{19\pi}{2}$ $\displaystyle \frac{19\pi}{2}$

$\frac{7\pi}{3}$ $\displaystyle \frac{7\pi}{3}$

$\frac{19\pi}{3}$ $\displaystyle \frac{19\pi}{3}$

$\frac{17\pi}{3}$ $\displaystyle \frac{17\pi}{3}$

Correct answer:

$\frac{19\pi}{3}$ $\displaystyle \frac{19\pi}{3}$

Explanation:

To convert between degrees and radians, you must use the following conversion factor 180 degrees = pi radians.

Therefore:

$\frac{1140}{1}*\frac{\pi}{180}=\frac{1140\pi}{180}=\frac{19\pi}{3}$ $\displaystyle \frac{1140}{1}*\frac{\pi}{180}=\frac{1140\pi}{180}=\frac{19\pi}{3}$

Report an Error

Example Question #2 : Angle Measures In Degrees And Radians

Please convert the following from degrees to radians: $315^{\circ}$ $\displaystyle 315^{\circ}$

Possible Answers:

$\frac{11\pi}6 {}$ $\displaystyle \frac{11\pi}6 {}$

$\frac{7\pi}{8}$ $\displaystyle \frac{7\pi}{8}$

$\pi$ $\displaystyle \pi$

$\frac{7\pi}{4}$ $\displaystyle \frac{7\pi}{4}$

$\frac{5\pi}{3}$ $\displaystyle \frac{5\pi}{3}$

Correct answer:

$\frac{7\pi}{4}$ $\displaystyle \frac{7\pi}{4}$

Explanation:

To convert from degrees to radians, multiply the input by: $\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

In this case:

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$ $(315^{\circ}) = \frac{7\pi}{4}$ $\displaystyle (315^{\circ}) = \frac{7\pi}{4}$

Report an Error

Example Question #9 : Convert Between Degrees And Radians

Please convert the following angle to degrees:

$\frac{7\pi }{6}$ $\displaystyle \frac{7\pi }{6}$

Possible Answers:

$210^\circ$ $\displaystyle 210^\circ$

$240^\circ$ $\displaystyle 240^\circ$

$180^\circ$ $\displaystyle 180^\circ$

$260^\circ$ $\displaystyle 260^\circ$

$176^\circ$ $\displaystyle 176^\circ$

Correct answer:

$210^\circ$ $\displaystyle 210^\circ$

Explanation:

To convert from radians to degrees, multiply the input by $\frac{180}{\pi}$ $\displaystyle \frac{180}{\pi}$.

In this case:

$\frac{180}{\pi}\cdot \left(\frac{7\pi}{6}\right) = 210^{\circ}$ $\displaystyle \frac{180}{\pi}\cdot \left(\frac{7\pi}{6}\right) = 210^{\circ}$

Report an Error

View Pre-Calculus Tutors

Anju
Certified Tutor

Jawaharlal Nehru Medical College, Bachelor of Science, Molecular Medicine. Pennsylvania State University-College of Medicine,...

View Pre-Calculus Tutors

Nnang
Certified Tutor

Columbia University in the City of New York, Bachelor of Science, Economics.

View Pre-Calculus Tutors

Vandana
Certified Tutor

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

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Philadelphia, SSAT Tutors in Washington DC, French Tutors in Miami, MCAT Tutors in Los Angeles, Algebra Tutors in New York City, Calculus Tutors in San Francisco-Bay Area, ACT Tutors in Houston, SAT Tutors in Atlanta, English Tutors in San Diego, MCAT Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Miami, MCAT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, GRE Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Philadelphia, SAT Courses & Classes in Miami

Popular Test Prep

MCAT Test Prep in Boston, MCAT Test Prep in Chicago, ACT Test Prep in Houston, MCAT Test Prep in Los Angeles, GMAT Test Prep in Phoenix, GMAT Test Prep in Seattle, ACT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Philadelphia

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

Precalculus : Angle Measures in Degrees and Radians

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Angle Measures In Degrees And Radians

Example Question #2 : Angle Measures In Degrees And Radians

Example Question #3 : Angle Measures In Degrees And Radians

Example Question #4 : Angle Measures In Degrees And Radians

Example Question #5 : Angle Measures In Degrees And Radians

Example Question #6 : Convert Between Degrees And Radians

Example Question #7 : Convert Between Degrees And Radians

Example Question #8 : Convert Between Degrees And Radians

Example Question #2 : Angle Measures In Degrees And Radians

Example Question #9 : Convert Between Degrees And Radians

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: