Call Now to Set Up Tutoring:

(888) 888-0446

New SAT Math - Calculator : Circles

Study concepts, example questions & explanations for New SAT Math - Calculator

Create An Account

All New SAT Math - Calculator Resources

2 Diagnostic Tests 27 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Radians

Change $\frac{4\pi }{3}$ angle to degrees.

Possible Answers:

$300^{\circ}$

$150^{\circ}$

$180^{\circ}$

$240^{\circ}$

Correct answer:

$240^{\circ}$

Explanation:

In order to change an angle into degrees, you must multiply the radian by $\frac{180^{\circ}}{\pi}$ .

Therefore, to solve:

$\frac{4\pi }{3} \cdot \frac{180^{\circ} }{\pi} = 240^{\circ}$

Report an Error

Example Question #563 : New Sat

Give in radians:

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

Possible Answers:

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

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

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

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

$x=\pi$

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 #564 : New Sat

Give in radians:

$x-\pi=120^{\circ}$

Possible Answers:

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

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

$x=\frac{5\pi}{6}$

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

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

Correct answer:

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

Explanation:

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

$120^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{2\pi}{3}$

Now we can write:

$x-\pi=120^{\circ}\Rightarrow x-\pi=\frac{2\pi}{3}\Rightarrow x=\frac{2\pi}{3}+\pi=\frac{5\pi}{3}$

Report an Error

Example Question #565 : New Sat

Give in degrees:

$\frac{3x+6\pi}{2}=4\pi$

Possible Answers:

$x=150^{\circ}$

$x=210^{\circ}$

$x=180^{\circ}$

$x=30^{\circ}$

$x=120^{\circ}$

Correct answer:

$x=120^{\circ}$

Explanation:

First we can find in radians:

$\frac{3x+6\pi}{2}=4\pi\Rightarrow 3x+6\pi=2\times 4\pi$

$\Rightarrow 3x+6\pi=8\pi\Rightarrow 3x=8\pi-6\pi$

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

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ . So we can write:

$x=\frac{2\pi}{3}\Rightarrow x=\frac{2\pi}{3}\times \frac{180^{\circ}}{\pi}=120^{\circ}$

Report an Error

Example Question #2 : Radians

Give in degrees:

$\frac{4x-\pi}{2}=3\pi$

Possible Answers:

$x=305^{\circ}$

$x=415^{\circ}$

$x=345^{\circ}$

$x=300^{\circ}$

$x=315^{\circ}$

Correct answer:

$x=315^{\circ}$

Explanation:

First we can find in radians:

$\frac{4x-\pi}{2}=3\pi\Rightarrow 4x-\pi=2\times 3\pi$

$\Rightarrow 4x-\pi=6\pi\Rightarrow 4x=6\pi+\pi$

$\Rightarrow 4x=7\pi\Rightarrow x=\frac{7\pi}{4}$

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ . So we can write:

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

Report an Error

Example Question #1 : Radians And Conversions

Give in radians:

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

Possible Answers:

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

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

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

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

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

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 #3 : Radians

Give in degrees:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}$

Possible Answers:

$x=36^{\circ}$

$x=40^{\circ}$

$x=60^{\circ}$

$x=90^{\circ}$

$x=30^{\circ}$

Correct answer:

$x=30^{\circ}$

Explanation:

First we can find in radians:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}\Rightarrow 2(\frac{\pi}{2}-x)=1(\frac{\pi}{2}+x)$

$\Rightarrow \pi-2x=\frac{\pi}{2}+x\Rightarrow \pi-\frac{\pi}{2}=3x$

$\Rightarrow 3x=\frac{\pi}{2}\Rightarrow x=\frac{\pi}{6}$

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ . So we can write:

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

Report an Error

Example Question #1 : Radians

Convert the angle $\frac{7\pi }{3}$ into degrees.

Possible Answers:

$315^{\circ}$

$210^{\circ}$

$500^{\circ}$

$420^{\circ}$

$840^{\circ}$

Correct answer:

$420^{\circ}$

Explanation:

To convert radians to degrees, use the conversion $\frac{180^{\circ}}{\pi }$ .

In this case:

$(\frac{7\pi }{3})*(\frac{180^{\circ}}{\pi }) = 420^{\circ}$

Report an Error

Example Question #4 : Radians

How many radians are in $300^\circ$ ?

Possible Answers:

$\pi\sqrt{3}$

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

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

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

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

Correct answer:

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

Explanation:

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

$\frac{300^\circ}{x}=\frac{180^\circ}{\pi}$

Cross-multiply and solve.

$300^\circ*\pi=180^\circ*x$

$\frac{300^\circ}{180^\circ}\pi=x$

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

Report an Error

Example Question #5 : Radians

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

Possible Answers:

$160^\circ$

$210^\circ$

$150^\circ$

$180^\circ$

$130^\circ$

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

View Tutors

Richard
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Chemistry. CUNY Brooklyn College, Master of Arts, Experimental Psychology.

View Tutors

Mark
Certified Tutor

View Tutors

Arnav
Certified Tutor

Rutgers University-Newark, Bachelor of Science, Biomedical Engineering.

All New SAT Math - Calculator Resources

2 Diagnostic Tests 27 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in San Francisco-Bay Area, French Tutors in San Francisco-Bay Area, Chemistry Tutors in Chicago, French Tutors in Los Angeles, Physics Tutors in Washington DC, Reading Tutors in San Diego, Computer Science Tutors in Dallas Fort Worth, Calculus Tutors in Los Angeles, Computer Science Tutors in San Diego, SAT Tutors in Houston

Popular Courses & Classes

MCAT Courses & Classes in Seattle, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Boston, SAT Courses & Classes in Phoenix, GMAT Courses & Classes in Denver, SSAT Courses & Classes in Boston, MCAT Courses & Classes in Denver, Spanish Courses & Classes in Houston

Popular Test Prep

MCAT Test Prep in Atlanta, ISEE Test Prep in Philadelphia, MCAT Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, MCAT Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Chicago, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Miami

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

New SAT Math - Calculator : Circles

Study concepts, example questions & explanations for New SAT Math - Calculator

All New SAT Math - Calculator Resources

Example Questions

Example Question #1 : Radians

Example Question #563 : New Sat

Example Question #564 : New Sat

Example Question #565 : New Sat

Example Question #2 : Radians

Example Question #1 : Radians And Conversions

Example Question #3 : Radians

Example Question #1 : Radians

Example Question #4 : Radians

Example Question #5 : Radians

All New SAT Math - Calculator Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: