Call Now to Set Up Tutoring:

(888) 888-0446

SAT Mathematics : Circles

Study concepts, example questions & explanations for SAT Mathematics

Create An Account

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Using Radians

Give in radians:

$\frac{x+\pi}{x-\pi}=30^{\circ}$

Possible Answers:

$x=\frac{\pi(\pi+6)}{\pi-6}$

$x=\frac{\pi+6}{\pi-6}$

$x=\frac{\pi(\pi+8)}{\pi-8}$

$x=\frac{\pi(\pi-6)}{\pi+6}$

Correct answer:

$x=\frac{\pi(\pi+6)}{\pi-6}$

Explanation:

First we need to convert degrees to radians by multiplying by $\frac{\pi}{180^{\circ}}$ :

$30^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{6}$

Now we can write:

$\frac{x+\pi}{x-\pi}=\frac{\pi}{6}\Rightarrow 6(x+\pi)=\pi(x-\pi)$

$\Rightarrow 6x+6\pi=x\pi-\pi^2\Rightarrow 6x-x\pi=-6\pi-\pi^2$

$\Rightarrow x(6-\pi)=-\pi(\pi+6)$

$\Rightarrow x=\frac{-\pi(\pi+6)}{6-\pi}=\frac{\pi(\pi+6)}{\pi-6}$

Report an Error

Example Question #2 : Using Radians

Give in radians:

$\frac{72^{\circ}-\pi}{2x-\pi}=3$

Possible Answers:

$x=\frac{2\pi}{5}$

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

$x=\frac{4\pi}{5}$

$x=\frac{3\pi}{5}$

Correct answer:

$x=\frac{2\pi}{5}$

Explanation:

First, we need to convert $72^{\circ}$ to radians by multiplying by $\frac{\pi}{180^{\circ}}$ :

$72^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{2\pi}{5}$

Now we can solve the following equation for :

$\frac{72^{\circ}-\pi}{2x-\pi}=3\Rightarrow \frac{\frac{2\pi}{5}-\pi}{2x-\pi}=3$

$\Rightarrow {\frac{2\pi}{5}-\pi}=3(2x-\pi)\Rightarrow \frac{2\pi-5\pi}{5}=6x-3\pi$

$\Rightarrow -3\pi=30x-15\pi\Rightarrow 30x=12\pi$

$\Rightarrow x=\frac{12\pi}{30}\Rightarrow x=\frac{2\pi}{5}$

Report an Error

Example Question #2 : Using Radians

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

Possible Answers:

$180^\circ$

$210^\circ$

$150^\circ$

$130^\circ$

Correct answer:

$150^\circ$

Explanation:

Since $180^\circ=\pi\ \text{radians}$ , we can solve by setting up a proportion:

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

Cross multiply and solve.

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

$\frac{900\pi}{6}=x*\pi$

$150\pi=x*\pi$

$\frac{150\pi}{\pi}=x$

$150^\circ=x$

Report an Error

Example Question #2 : Using Radians

Change the following expression to degrees:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}$

Possible Answers:

$90^{\circ}$

$120^{\circ}$

$75^{\circ}$

$60^{\circ}$

Correct answer:

$60^{\circ}$

Explanation:

First, we need to simplify the expression:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}=\frac{\frac{2\pi-\pi}{6}}{\frac{2+1}{6}}=\frac{\pi}{3}$

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

$\frac{\pi}{3}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{3}=60^{\circ}$

Report an Error

Example Question #4 : Using Radians

Convert the following expression to radians:

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

Possible Answers:

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

$\frac{\pi}{36}$

$\frac{\pi}{30}$

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

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 #4 : Using Radians

Simplify and give the following expression in degrees:

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

Possible Answers:

$420^{\circ}$

$350^{\circ}$

$450^{\circ}$

$480^{\circ}$

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 #5 : Using Radians

Convert $\frac{7\pi}{4}$ radians into degrees.

Possible Answers:

$345$^{\circ}$$

$285$^{\circ}$$

$315$^{\circ}$$

$225$^{\circ}$$

Correct answer:

$315$^{\circ}$$

Explanation:

Recall the definition of "radians" derived from the unit circle:

$180$^{\circ}$ = \pi rad$

The quantity of radians given in the problem is $\frac{7\pi}{4}$ . All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by $\Theta$ and set up a proportion equation using the aforementioned definition relating radians to degrees:

$\frac{180^{\circ}}{\Theta} = \frac{\pi rad}{\frac{7\pi}{4} rad}$

Cross-multiply the denominators in these fractions to obtain:

$1260^{\circ}\pi rad=4\Theta\pi rad$

$315^{\circ}\pi rad =\Theta\pi rad$ .

Canceling like terms in these equations yields

$\Theta = 315^{\circ}$

Hence, the correct angle measure of $\frac{7\pi}{4}$ in degrees is $315^{\circ}$ .

Report an Error

Example Question #6 : Using Radians

$\frac{37\pi}{18}$ radians is equivalent to how many degrees?

Possible Answers:

$350^\circ$

$185^\circ$

$370^\circ$

$10^\circ$

Correct answer:

$370^\circ$

Explanation:

1 radian is equal to $\frac{180}{\pi}$ degrees. Using this conversion factor,

$\frac{37\pi}{18}\times\frac{180}{\pi}=37\times10=370$ .

Report an Error

Example Question #7 : Using Radians

Simplify your answer.

Convert $45^{\circ}$ to radians:

Possible Answers:

$\frac{\pi }{2}$

$\frac{\pi }{8}$

$\frac{\pi }{4}$

$\frac{1 }{4}$

Correct answer:

$\frac{\pi }{4}$

Explanation:

We know that:

$360^{\circ}=2\pi$ Radians

since the giving angle was in degrees then we multiply

$45^{\circ}*\frac{\pi}{180^{\circ}}= \frac{\pi}{4}$

Report an Error

Example Question #9 : Using Radians

Give your answer in terms of $\pi$ .

Convert $165^{\circ}$ to radians:

Possible Answers:

$\frac{11\pi}{12}$

$\frac{12\pi}{11}$

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

$\frac{11\pi}{24}$

Correct answer:

$\frac{11\pi}{12}$

Explanation:

To convert degrees to radians, we need to multiply the given degree by $\frac{\pi}{180^{\circ}}$ .

$165*^{\circ}\frac{\pi}{180^{\circ}}=\frac{165\pi}{180}$

To simplify, we get:

$\frac{11\pi}{12}$

Report an Error

View Tutors

Melissa
Certified Tutor

Salem College, Bachelor in Arts, Mass Communications.

View Tutors

Trennon
Certified Tutor

Appalachian State University, Bachelor of Science, Actuarial Science. Appalachian State University, Master of Science, Statis...

View Tutors

Humayun
Certified Tutor

New York University, Master's/Graduate, International Relations.

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Washington DC, Physics Tutors in New York City, Reading Tutors in Dallas Fort Worth, Chemistry Tutors in San Diego, Statistics Tutors in Phoenix, Computer Science Tutors in Seattle, GMAT Tutors in San Diego, SSAT Tutors in Seattle, MCAT Tutors in Washington DC, Computer Science Tutors in Philadelphia

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Seattle, ACT Courses & Classes in New York City, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Boston, ACT Courses & Classes in Washington DC, SAT Courses & Classes in Phoenix, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

LSAT Test Prep in Denver, GRE Test Prep in Boston, SSAT Test Prep in Denver, SAT Test Prep in Boston, ACT Test Prep in New York City, GRE Test Prep in Atlanta, ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, ISEE 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

SAT Mathematics : Circles

Study concepts, example questions & explanations for SAT Mathematics

All SAT Mathematics Resources

Example Questions

Example Question #1 : Using Radians

Example Question #2 : Using Radians

Example Question #2 : Using Radians

Example Question #2 : Using Radians

Example Question #4 : Using Radians

Example Question #4 : Using Radians

Example Question #5 : Using Radians

Example Question #6 : Using Radians

Example Question #7 : Using Radians

Example Question #9 : Using Radians

All SAT Mathematics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: