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 #1 : Find The Length Of The Arc Of A Circle Using Radians

Find the length of an arc of a circle if the radius is and the angle is $\frac{\pi}{4}$ radians.

Possible Answers:

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

$\frac{\pi}{2}$

$\frac{\pi}{4}$

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

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

Correct answer:

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

Explanation:

Write the formula to find the arc length given the angle in radians.

$s=r\theta$

Substitute the radius and angle.

$s=3\left(\frac{\pi}{4}\right)=\frac{3\pi}{4}$

Report an Error

Example Question #2 : Find The Length Of The Arc Of A Circle Using Radians

Find the length of a circular arc if the radius is , with an angle of $\frac{\pi}{2}$ .

Possible Answers:

$\pi$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$2\pi$

Correct answer:

$\pi$

Explanation:

Write the formula to find the length of an arc given the angle in radians.

$s=r\theta$

Substitute the radius and the angle in order to find the length of the arc.

$s=2\left(\frac{\pi}{2}\right)=\pi$

Report an Error

Example Question #1 : Find The Length Of The Arc Of A Circle Using Radians

If circle has a radius of ${}\frac{5}{\pi}$ fathoms and sector BFG has a central angle of $\pi$ . What is the measure of arc ?

Possible Answers:

$\frac{5}{\pi} fathoms$

5 radians

$5\pi fathoms$

5 fathoms

10 fathoms

Correct answer:

5 fathoms

Explanation:

To find the length of an arc, use the following formula:

$\frac{\theta }{2\pi}\cdot 2\pi r=arc_{length}$

We are given the radius, as well as our central angle, so plug in what we know and simplify

$\frac{\pi }{2\pi}\cdot 2\pi \cdot \frac{5}{\pi}=\frac{1}{2}\cdot 2\cdot 10=5$

So our answer is 5 fathoms

Report an Error

Example Question #3 : Find The Length Of The Arc Of A Circle Using Radians

Find the length of an arc of a circle if the radius is and the angle is $\frac{5\pi}{4}$ .

Possible Answers:

$\frac{15\pi}{4}$

$\frac{15\pi}{8}$

$\frac{15\pi}{2}$

$15\pi$

$30\pi$

Correct answer:

$\frac{15\pi}{2}$

Explanation:

Write the formula for arc length.

$s=r\theta$

Substitute the known radius and angle.

$s=6\left(\frac{5\pi}{4}\right)=\frac{15\pi}{2}$

Report an Error

Example Question #5 : Find The Length Of The Arc Of A Circle Using Radians

When CERN was designing its Large Hadron Collider, they needed to run a cable from the control house to a spot $\frac{\pi}{3}$ radians around the circle. If the Large Hadron Colider has a radius of $4.29\:km$ , what length of cable will be necessary to reach the sensor?

Possible Answers:

$4.29\:km$

$4.5\:km$

$6.7\:km$

$2.3\:km$

Correct answer:

$4.5\:km$

Explanation:

When CERN was designing its Large Hadron Collider, they needed to run a cable from the control house to a spot $\frac{\pi}{3}$ radians around the circle. If the Large Hadron Colider has a radius of , what length of cable will be necessary to reach the sensor?

The formula for length of an arc is as follows:

$Arc=\frac{Central\angle }{2\pi}*2\pi r$

Thus, to find the measure of the central angle, what we are really doing is multiplying the total circumference by the fractional part of the circle we are interested in. In this case, we already have the radius and the central angle, we just need to plug and chug.

$Arc=\frac{\frac{\pi}{3}}{2\pi}*2\pi*4.29=\frac{\pi}{3}*4.29=4.49\approx4.5\:km$

So our answer is:

$4.5\:km$

Report an Error

Example Question #6 : Find The Length Of The Arc Of A Circle Using Radians

If a circle has a circumference of 310 kilometers, find the length of the arc associated with a central angle of $\frac{3\pi}{4}$ radians.

Possible Answers:

116km

233km

310km

2920km

Correct answer:

116km

Explanation:

If a circle has a circumference of 310 kilometers, find the length of the arc associated with a central angle of $\frac{3\pi}{4}$ radians

Recall that arc length can be found via the following:

$Arc=\frac{\measuredangle }{2\pi}*2\pi r$

Upon closer examination, we see that the formula is really two parts. The first part gives us the fractional area of the circle we care about. The second part is simply the circumference. This means that if we multiply the whole circumference by the fraction that we care about, we will just get the arc length of the portion we care about.

So, plug it in and go!

$Arc=\frac{\frac{3\pi}{4}}{2\pi}* (310km)$

Looks messy, but we'll simplify it.

$Arc=\frac{\frac{3\pi}{4}}{ 2\pi}* (310km)=\frac{3}{8}*310km$

$Arc=\frac{3}{8}*310km\approx116km$

So our answer is 116km.

Report an Error

Example Question #7 : Find The Length Of The Arc Of A Circle Using Radians

Find the arc length of a circle with circumference $10\pi$ that goes from 0^o to $135^\circ$ around its center.

Possible Answers:

$A=\frac{15\pi}{4}$

$A=\frac{25\pi}{4}$

$A=\frac{10\pi}{3}$

A=675

Correct answer:

$A=\frac{15\pi}{4}$

Explanation:

Remember that arc length of a circle is given by:

$A=\theta r$ , where $\theta$ is angle made by connecting the radius to the two ends of the arc, given in radians. is the radius.

To get $\theta$ , we convert from degrees to radians.

$\theta = 135deg\cdot\frac{\pi rad}{180deg}=\frac{3\pi}{4}$

To get the radius we convert from the circumference

$r=\frac{C}{2\pi}=\frac{10\pi}{2\pi}=5$

$A=\frac{3\pi}{4}\cdot5= \frac{15\pi}{4}$

Report an Error

Example Question #2 : Find The Length Of The Arc Of A Circle Using Radians

C2_img1

If the length of is and $\angle O=\frac{\pi}{5}$ , which of the following is closest to the length of minor arc ?

Possible Answers:

1.88m

1.9m

1.8m

Correct answer:

1.88m

Explanation:

The formula for arc length of a circle, given in radians, is $s=\theta \cdot r$ , where is the arc length.

Then, plug in the givens: $s=\frac{\pi}{5}\cdot 3$ and simplify: s=1.884955592 .

Then round to the appropriate placement: s=1.88 .

Therefore, the arc length of is 1.88m .

Report an Error

Example Question #1 : Find The Area Of A Sector Using Radians

Find the area of a sector if the radius of the circle is 4, and the angle of the sector is $\pi$ radians.

Possible Answers:

$4\pi$

$16\pi$

$2\pi$

$8\pi$

$12\pi$

Correct answer:

$8\pi$

Explanation:

Write the formula for the area of the sector in radians.

$A=\frac{1}{2}r^2 \theta$

Substitute the radius and theta.

$A=\frac{1}{2}(4)^2 (\pi)= 8\pi$

Report an Error

Example Question #1 : Find The Area Of A Sector Using Radians

Find the area of a sector if the radius is 1 and the angle of sector is $2\pi$ radians.

Possible Answers:

$2\pi$

$\frac{\pi}{2}$

$\pi$

Correct answer:

$\pi$

Explanation:

Write the formula for the area of the sector in radians and substitute the given values.

$A=\frac{1}{2}r^2 \theta = \frac{1}{2}(1)^2(2\pi)=\pi$

Report an Error

View Pre-Calculus Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Pre-Calculus Tutors

Samarth
Certified Tutor

Maharaja Sayajirao University of Baroda, Bachelor of Engineering, Mechanical Engineering. Concordia University-Seward, Master...

View Pre-Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

All Precalculus Resources

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

Popular Subjects

English Tutors in Atlanta, Biology Tutors in Chicago, Biology Tutors in Houston, GRE Tutors in Denver, Reading Tutors in San Francisco-Bay Area, English Tutors in Miami, GMAT Tutors in Dallas Fort Worth, French Tutors in Seattle, Calculus Tutors in Atlanta, French Tutors in Philadelphia

Popular Courses & Classes

MCAT Courses & Classes in Miami, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Seattle, SSAT Courses & Classes in San Diego, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in San Diego, ACT Courses & Classes in Miami, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Los Angeles

Popular Test Prep

ISEE Test Prep in Philadelphia, MCAT Test Prep in Houston, MCAT Test Prep in Denver, SAT Test Prep in Boston, MCAT Test Prep in Chicago, MCAT Test Prep in New York City, GRE Test Prep in Denver, ACT Test Prep in Phoenix, LSAT Test Prep in Houston, GRE Test Prep in Phoenix

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 #1 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #2 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #1 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #3 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #5 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #6 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #7 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #2 : Find The Length Of The Arc Of A Circle Using Radians

Example Question #1 : Find The Area Of A Sector Using Radians

Example Question #1 : Find The Area Of A Sector Using Radians

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: