We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : The Unit Circle and Radians

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Trigonometry

How many degrees are in $\frac{2\pi}{3}$ radians?

Possible Answers:

$150^\circ$

$120^\circ$

$60^\circ$

$210^\circ$

$180^\circ$

Correct answer:

$120^\circ$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{x^\circ}{\frac{2\pi}{3}}=\frac{180^\circ}{\pi}$

Cross multiply:

$x^\circ*\pi=180^\circ*\frac{2\pi}{3}$

Notice that the $\pi$ 's cancel out:

$x^\circ=180^\circ*\frac{2}{3}$

$x^\circ=120^\circ$

Report an Error

Example Question #21 : The Unit Circle And Radians

How many degrees are in $\frac{5\pi}{6}$ radians?

Possible Answers:

$210^\circ$

$30^\circ$

$390^\circ$

$240^\circ$

$150^\circ$

Correct answer:

$150^\circ$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{x^\circ}{\frac{5\pi}{6}}=\frac{180^\circ}{\pi}$

Cross multiply:

$x^\circ*\pi=180^\circ*\frac{5\pi}{6}$

Notice that the $\pi$ 's cancel out:

$x^\circ=180^\circ*\frac{5}{6}$

$x^\circ=150^\circ$

Report an Error

Example Question #41 : Trigonometry

How many radians are in $120^\circ$ ?

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

$6\pi$

$\frac{3\pi}{2}$

$\frac{2\pi}{3}$

Correct answer:

$\frac{2\pi}{3}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{120^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$120^\circ*\pi=180^\circ*x$

Isolate :

$\frac{120^\circ}{180^\circ}\pi=x$

$\frac{2\pi}{3}=x$

Report an Error

Example Question #23 : The Unit Circle And Radians

How many radians are in $360^\circ$ ?

Possible Answers:

$\pi^2$

$2\pi$

$\pi$

$\frac{\pi}{2}$

$4\pi$

Correct answer:

$2\pi$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{360^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$360^\circ*\pi=180^\circ*x$

Isolate :

$\frac{360^\circ}{180^\circ}\pi=x$

$2\pi=x$

Report an Error

Example Question #24 : The Unit Circle And Radians

How many radians are in $405^\circ$ ?

Possible Answers:

$\frac{4\pi}{9}$

$\frac{9\pi}{4}$

$\frac{2\pi}{9}$

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

$\frac{\pi}{4}$

Correct answer:

$\frac{9\pi}{4}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{405^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$405^\circ*\pi=180^\circ*x$

Isolate :

$\frac{405^\circ}{180^\circ}\pi=x$

$\frac{9\pi}{4}=x$

Report an Error

Example Question #11 : Understanding Radians And Conversions

How many radians are in $81^\circ$ ?

Possible Answers:

$\frac{9\pi}{10}$

$2\pi+9$

$\frac{20\pi}{9}$

$\frac{9\pi}{20}$

$180\pi$

Correct answer:

$\frac{9\pi}{20}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{81^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$81^\circ*\pi=180^\circ*x$

Isolate :

$\frac{81^\circ}{180^\circ}\pi=x$

Reduce:

$\frac{9\pi}{20}=x$

Report an Error

Example Question #12 : Understanding Radians And Conversions

How many radians are in $90^\circ$ ?

Possible Answers:

$\frac{\pi}{2}$

$\frac{2\pi}{3}$

$\pi$

$\frac{\pi}{4}$

$2\pi$

Correct answer:

$\frac{\pi}{2}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{90^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$90^\circ*\pi=180^\circ*x$

Isolate :

$\frac{90^\circ}{180^\circ}\pi=x$

Reduce:

$\frac{\pi}{2}=x$

Report an Error

Example Question #21 : The Unit Circle And Radians

How many degrees are in $2\pi$ radians?

Possible Answers:

$720^\circ$

$360^\circ$

$180^\circ$

$90^\circ$

$540^\circ$

Correct answer:

$360^\circ$

Explanation:

Remember, $180^\circ=\pi$ radians, so $2\pi$ radians would correspond to $2*180^\circ=360^\circ$ .

Report an Error

Example Question #26 : The Unit Circle And Radians

How many radians are in $180^\circ$ ?

Possible Answers:

$\pi$

$2\pi$

$\frac{\pi}{2}$

$\frac{2\pi}{3}$

$\frac{3\pi}{2}$

Correct answer:

$\pi$

Explanation:

The ratio between radians and degrees is $180^\circ=\pi$ radians.

Since the question asks us about $180^\circ$ , the conversion tells us it will be $\pi$ radians.

Report an Error

Example Question #21 : The Unit Circle And Radians

How many degrees are in $\frac{3}{4}\pi$ radians?

Possible Answers:

$135^\circ$

$450^\circ$

$225^\circ$

$90^\circ$

$270^\circ$

Correct answer:

$135^\circ$

Explanation:

The ratio between radians and degrees is $180^\circ=\pi$ radians.

That means we can set up a proportion:

$\frac{x}{\frac{3}{4}\pi}=\frac{180^\circ}{\pi}$

$x\pi=180^\circ*\frac{3}{4}\pi$

Notice that the $\pi$ 's cancel out.

$x=180^\circ*\frac{3}{4}$

$x=135^\circ$

Report an Error

View Tutors

Aditi
Certified Tutor

Georgetown University, Bachelor, International Politics. University of Pennsylvania, Professional (JD, MD, DMD, etc), J.D..

View Tutors

Tim
Certified Tutor

University of Western States, Juris Doctor, Chiropractic (DC). Logan University, Master of Science, Human Nutrition.

View Tutors

Shadwaynn
Certified Tutor

Indiana University/Purdue University at Fort Wayne, Bachelor, Elementary Education. Indiana University/Purdue University at F...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Washington DC, Physics Tutors in Dallas Fort Worth, Statistics Tutors in Houston, Reading Tutors in New York City, MCAT Tutors in Houston, French Tutors in Atlanta, Biology Tutors in New York City, Chemistry Tutors in Philadelphia, English Tutors in New York City, Math Tutors in Boston

Popular Courses & Classes

ISEE Courses & Classes in Houston, ACT Courses & Classes in San Diego, SAT Courses & Classes in Chicago, GRE Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Boston, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Houston

Popular Test Prep

SSAT Test Prep in Atlanta, ACT Test Prep in San Diego, LSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Diego, ISEE Test Prep in Houston, LSAT Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Miami, ISEE Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area

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

High School Math : The Unit Circle and Radians

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #41 : Trigonometry

Example Question #21 : The Unit Circle And Radians

Example Question #41 : Trigonometry

Example Question #23 : The Unit Circle And Radians

Example Question #24 : The Unit Circle And Radians

Example Question #11 : Understanding Radians And Conversions

Example Question #12 : Understanding Radians And Conversions

Example Question #21 : The Unit Circle And Radians

Example Question #26 : The Unit Circle And Radians

Example Question #21 : The Unit Circle And Radians

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: