Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Unit Circle and Radians

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

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #31 : Unit Circle And Radians

Convert the following expression to radians:

$\frac{45^{\circ}+30^{\circ}}{45-30}$

Possible Answers:

$\frac{5\pi}{36}$

$\frac{\pi}{30}$

$\frac{\pi}{12}$

$\frac{7\pi}{36}$

$\frac{\pi}{36}$

Correct answer:

$\frac{\pi}{36}$

Explanation:

First we need to simplify the expression:

$\frac{45^{\circ}+30^{\circ}}{45-30}=\frac{75^{\circ}}{15}=5^{\circ}$

In order to change degrees to radians, we need to multiply by $\frac{\pi}{180^{\circ}}$ :

$5^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{36}$

Report an Error

Example Question #31 : Unit Circle And Radians

Change $270^{\circ}$ to radians.

Possible Answers:

$\pi$

$2\pi$

$1.5\pi$

$3\pi$

$2.5\pi$

Correct answer:

$1.5\pi$

Explanation:

In order to change degrees to radians we need to multiply degrees by $\frac{\pi}{180^{\circ}}$ :

$270^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{3\pi}{2}=1.5\pi$

Report an Error

Example Question #582 : New Sat

Convert one radian to degrees.

Possible Answers:

$57.3^{\circ}$

$60^{\circ}$

$50^{\circ}$

$67.3^{\circ}$

$47.3^{\circ}$

Correct answer:

$57.3^{\circ}$

Explanation:

In order to change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ :

$1\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{\pi}\approx 57.3^{\circ}$

Report an Error

Example Question #583 : New Sat

Convert one degree to radians.

Possible Answers:

$\frac{\pi}{60}$

$\frac{\pi}{120}$

$\frac{\pi}{90}$

$\frac{\pi}{180}$

$\pi$

Correct answer:

$\frac{\pi}{180}$

Explanation:

In order to change degrees to radians we need to multiply the degrees by $\frac{\pi}{180^{\circ}}$ :

$1^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{180}$

Report an Error

Example Question #21 : Circles

Simplify and give the followoing expression in degrees:

$2\pi-\frac{\pi}{4}$

Possible Answers:

$285^{\circ}$

$300^{\circ}$

$325^{\circ}$

$315^{\circ}$

$270^{\circ}$

Correct answer:

$315^{\circ}$

Explanation:

First we need to simplify the expression:

$2\pi-\frac{\pi}{4}=\frac{8\pi-\pi}{4}=\frac{7\pi}{4}$

Then multiply by $\frac{180^{\circ}}{\pi}$ :

$\frac{7\pi}{4}\times \frac{180^{\circ}}{\pi}=\frac{7\times 180^{\circ}}{4}=315^{\circ}$

Report an Error

Example Question #21 : Radians And Conversions

Simplify and give the followoing expression in degrees:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}$

Possible Answers:

$450^{\circ}$

$350^{\circ}$

$480^{\circ}$

$380^{\circ}$

$420^{\circ}$

Correct answer:

$450^{\circ}$

Explanation:

First we need to simplify the expression:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}=\frac{\frac{4\pi+\pi}{14}}{\frac{1}{7}}=\frac{5\pi}{2}$

Then multiply by $\frac{180^{\circ}}{\pi}$ :

$\frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=\frac{5\times 180^{\circ}}{2}=450^{\circ}$

Report an Error

Example Question #23 : Radians

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

Possible Answers:

$30^\circ$

$120^\circ$

$250^\circ$

$150^\circ$

$60^\circ$

Correct answer:

$120^\circ$

Explanation:

Use the conversion $\pi \textup{ radians}= 180\textup{ degrees}$ .

Since we are converting radians to degrees, multiply by 180 degrees and divide by $\pi$ radians.

$\frac{2\pi}{3} \textup{ radians}\left(\frac{180 \textup{ degrees}}{\pi\textup{ radian}}\right)= 120\textup{ degrees}$

Report an Error

Example Question #21 : Radians And Conversions

How many degrees is 3 radians?

Possible Answers:

$189^{\circ}$

$150^{\circ}$

$156^{\circ}$

None of these other answers.

$172^{\circ}$

Correct answer:

$172^{\circ}$

Explanation:

When going from radians to degrees one multiplies by the conversion factor

$\frac{180^{\circ}}{\pi rad}$ .

The radians cancel and the answer is left in degrees.

$3\hspace{1mm}{\color{Red} rad}\cdot\frac{180^{\circ}}{\pi {\color{Red} rad}}=\frac{540^\circ}{\pi}=172^{\circ}$

Report an Error

Example Question #22 : Radians And Conversions

Convert to radians: 33^o

Possible Answers:

0.189

0.058

0.183

1.736

0.576

Correct answer:

0.576

Explanation:

To convert to radians, set up the ratio $\frac{180}{\pi } = \frac{33} { x}$ :

$180 x = 33 \pi$

$x = 33 \pi \div 180 \approx 0.576$

Report an Error

Example Question #23 : Radians And Conversions

Convert to degrees: $\frac{2 \pi }{7}$

Possible Answers:

16.37^o

51.43^o

147.58^o

0.016^o

Correct answer:

51.43^o

Explanation:

To convert, divide by $\pi$ and multiply by 180 :

$\frac{2 \pi }{7 } \div \pi = \frac{2}{7}$

$\frac{2}{7} \cdot 180 \approx 51.47^o$

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

View Trigonometry Tutors

Jitendra
Certified Tutor

BHU, Bachelor, Mathematics.

View Trigonometry Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Trigonometry Tutors

Matthew
Certified Tutor

University of Maryland Eastern Shore, Bachelor of Science, Mathematics. Delaware State University, Doctor of Philosophy, Appl...

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

MCAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Boston, SSAT Courses & Classes in San Diego, ACT Courses & Classes in Denver, MCAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Boston, ACT Courses & Classes in Chicago, LSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Boston

Popular Test Prep

GRE Test Prep in New York City, GMAT Test Prep in Chicago, GMAT Test Prep in Boston, ACT Test Prep in Chicago, ACT Test Prep in Denver, SAT Test Prep in New York City, GRE Test Prep in Atlanta, ISEE Test Prep in New York City, SSAT Test Prep in New York City, ISEE 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 : Unit Circle and Radians

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #31 : Unit Circle And Radians

Example Question #31 : Unit Circle And Radians

Example Question #582 : New Sat

Example Question #583 : New Sat

Example Question #21 : Circles

Example Question #21 : Radians And Conversions

Example Question #23 : Radians

Example Question #21 : Radians And Conversions

Example Question #22 : Radians And Conversions

Example Question #23 : Radians And Conversions

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: