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 #11 : Convert Between Degrees And Radians

Convert $\frac{3\pi}{7}$ radians to degrees. Round to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

In order to convert from radians to degrees, we will need to know how many degrees are in a radian.

$\pi \textup{ radians} = 180 \textup{ degrees}$

Substitute 180 as a replacement for $\pi$ .

$\frac{3\pi}{7} = \frac{3\times 180}{7} = \frac{540}{7} = 77.1429$

The correct answer is .

Report an Error

Example Question #11 : Angle Measures In Degrees And Radians

Convert $50^{\circ}$ to radians.

Possible Answers:

$\frac{5\pi }{21}$

$\frac{\pi }{3}$

$\frac{5\pi }{18}$

$\frac{9\pi }{14}$

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

Correct answer:

$\frac{5\pi }{18}$

Explanation:

To convert degrees to radians we must recall the conversion factor. Remember that $360^\circ=2\pi$ .

Therefore, we can create the following fraction and solve for the missing variable.

$\frac{50^{\circ}}{360^{\circ}}=\frac{x}{2\pi }$

$360x=2\pi (50)$

$x=\frac{5\pi }{18}$

Report an Error

Example Question #11 : Angle Measures In Degrees And Radians

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be $114^{\circ}$ . What is the angle in radians?

Possible Answers:

$0.3\bar{3}\pi \:\uptext{radians}$

$6.\bar{3}\pi\:\uptext{ radians}$

$0.3\bar{6}\pi\:\uptext{radians}$

$0.6\bar{3}\pi \:\uptext{radians}$

Correct answer:

$0.6\bar{3}\pi \:\uptext{radians}$

Explanation:

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be $114^{\circ}$ . What is the angle in radians?

To convert from degrees to radians, use the following formula:

$\frac{d\pi}{180}=r$

Where and stand for degrees and radians, respectively.

$r=\frac{114\pi}{180}=0.6\bar{3}\pi\:\uptext{radians}$

So we get

$0.6\bar{3}\pi \:\uptext{radians}$

Report an Error

Example Question #91 : Trigonometric Functions

Terry is running around a circular track. If he covers $\frac{7\pi}{6} radians$ in 120 seconds, how many degrees has he covered?

Possible Answers:

$255^{\circ}$

$150^{\circ}$

$270^{\circ}$

$210^{\circ}$

Correct answer:

$210^{\circ}$

Explanation:

Terry is running around a circular track. If he covers $\frac{7\pi}{6} radians$ in 120 seconds, how many degrees has he covered?

To convert from radians to degrees, use the following helpful formula:

$d=\frac{180r}{\pi}$

Where r and d are our desired angle measure in radians and degrees, respectively.

So, we have r, plug in and simplify to get d!

$d=\frac{180\frac{7\pi}{6} }{\pi}=\frac{30*7\pi}{\pi}=210^{\circ}$

Making our answer:

$210^{\circ}$

Report an Error

Example Question #11 : Angle Measures In Degrees And Radians

While SCUBA diving as part of a search and rescue diving operation, Daniel is responsible for covering a sector which represents $\frac{5\pi}{6}$ radians. What is this angle in degrees?

Possible Answers:

$210^{\circ}$

$180^{\circ}$

$250^{\circ}$

$150^{\circ}$

Correct answer:

$150^{\circ}$

Explanation:

While SCUBA diving as part of a search and rescue diving operation, Daniel is responsible for covering a sector which represents $\frac{5\pi}{6}$ radians. What is this angle in degrees?

Recall the following formula for converting radians to degrees:

$d=\frac{180r}{\pi}$

Where d and r are angle measures in degrees and radians, respectively.

So, we are given a value in radians and asked to find it in degrees. Plug in to the above formula to find the answer!

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

So our answer is: $150^{\circ}$

Report an Error

Example Question #11 : Angle Measures In Degrees And Radians

Determine the value of $225^\circ$ in radians.

Possible Answers:

$\frac{5\pi}{4}rad$

$\frac{40500}{\pi}rad$

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

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

Correct answer:

$\frac{5\pi}{4}rad$

Explanation:

To convert from degrees to radians, you do:

$225deg\cdot \frac{(\pi) rad}{180 deg}= \frac{(45\cdot5)\cdot\pi}{45\cdot4} rad= \frac{5\pi}{4} rad$

Report an Error

Example Question #12 : Angle Measures In Degrees And Radians

Convert the following to radians.

$270^{\circ}$

Possible Answers:

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

$\frac{3}{\pi}$

$\frac{\pi}{3}$

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

Correct answer:

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

Explanation:

To solve, use the conversion factor $\frac{\pi{radians}}{180^{\circ}}$ . Thus,

$\frac{270^{\circ}}{1}\cdot \frac{\pi{radians}}{180^{\circ}}=\frac{270\pi}{180}=\frac{3\pi}{2}$

Report an Error

Example Question #321 : Pre Calculus

Convert $660^{\circ}$ to radians.

Possible Answers:

$\frac{11\pi }{3}$

$\frac{13\pi }{3}$

$\frac{66\pi }{7}$

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

$\frac{111\pi }{3}$

Correct answer:

$\frac{11\pi }{3}$

Explanation:

To convert from degrees to radians, you must multiply by $\frac{\pi }{180}$ : $660\cdot \frac{\pi }{180}$ . Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.

Thus, your answer is $\frac{11\pi }{3}$ .

Report an Error

Example Question #13 : Angle Measures In Degrees And Radians

Convert $\frac{8\pi }{3}$ to degrees.

Possible Answers:

$480^{\circ}$

$400^{\circ}$

$550^{\circ}$

$280^{\circ}$

$440^{\circ}$

Correct answer:

$480^{\circ}$

Explanation:

To convert from radians to degrees, you must multiply by $\frac{180}{\pi }$ so that you then get $\frac{8\pi }{3}\cdot \frac{180}{\pi }$ . Then, simplify and multiply straight across so that your answer is $480^{\circ}$ .

Report an Error

Example Question #14 : Angle Measures In Degrees And Radians

$\frac{11\pi}{9}$ radians is equivalent to how many degrees?

Possible Answers:

190

225

210

185

220

Correct answer:

220

Explanation:

The value of $\pi$ radians equal 180 degrees. Substitute and solve.

$\frac{11\pi}{9}=\frac{11\cdot 180}{9}=\frac{1980}{9}=220$

Report an Error

View Pre-Calculus Tutors

Mohammad
Certified Tutor

Jamia Millia Islamia, Master of Science, Physics.

View Pre-Calculus Tutors

Tom
Certified Tutor

University of Wisconsin-Madison, Bachelor of Science, Atmospheric Sciences and Meteorology. Embry-Riddle Aeronautical Univers...

View Pre-Calculus Tutors

Jaahanava
Certified Tutor

University of Windsor, Master's/Graduate, Computer Science .

All Precalculus Resources

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

Popular Subjects

ISEE Tutors in Denver, ISEE Tutors in Phoenix, Math Tutors in Los Angeles, LSAT Tutors in Seattle, English Tutors in Washington DC, MCAT Tutors in Seattle, GRE Tutors in Chicago, Statistics Tutors in Chicago, GMAT Tutors in Dallas Fort Worth, Chemistry Tutors in San Diego

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Boston, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Atlanta, GRE Courses & Classes in Philadelphia, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, Spanish Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in Philadelphia, LSAT Test Prep in San Diego, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in New York City, ACT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in New York City, ISEE Test Prep in Miami, ISEE Test Prep in Houston, GMAT Test Prep in Los Angeles

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 #11 : Convert Between Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #91 : Trigonometric Functions

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #12 : Angle Measures In Degrees And Radians

Example Question #321 : Pre Calculus

Example Question #13 : Angle Measures In Degrees And Radians

Example Question #14 : Angle Measures In Degrees And Radians

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: