Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Polar

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Polar Calculations

Convert the cartesian point (1,1) into polar coordinates.

Possible Answers:

$(-8, \pi)$

$(\sqrt3/2, \pi/6)$

(-1,1)

$(\sqrt2, \pi/4)$

Correct answer:

$(\sqrt2, \pi/4)$

Explanation:

Cartesian coordinates are written in the form (x,y) .

In this problem, x=1 and y=1 .

Using the conversion formulas $r=\sqrt{x^2+y^2}$ and $\theta=tan^{-1}\left ( y/x\right )$ ,

$r=\sqrt{x^2+y^2}=\sqrt{1^2+1^2}=\sqrt2$

$\theta=tan^{-1}\left ( y/x\right )=tan^{-1}\left ( 1\right )=\pi/4$

The polar point is $(\sqrt2, \pi/4)$ .

Report an Error

Example Question #12 : Polar Calculations

Convert the cartesian point (-3,4) into polar coordinates.

Possible Answers:

(-3,4)

$(\sqrt3/2, \pi/6)$

(-4,2.584)

(5,5.356)

Correct answer:

(5,5.356)

Explanation:

Cartesian coordinates are written in the form (x,y) .

In this problem, x=-3 and y=4 .

Using the conversion formulas $r=\sqrt{x^2+y^2}$ and $\theta=tan^{-1}\left ( y/x\right )$ ,

$r=\sqrt{x^2+y^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

$\theta=tan^{-1}\left ( y/x\right )=tan^{-1}\left ( -4/3\right )=-0.927=5.356$

The polar point is (5,5.356) .

Report an Error

Example Question #841 : Calculus Ii

Convert the cartesian point (5, 12) into polar coordinates.

Possible Answers:

(5, 12)

(12,3.746)

(13,1.176)

(-3,4)

Correct answer:

(13,1.176)

Explanation:

Cartesian coordinates are written in the form (x,y) .

In this problem, x=5 and y=12 .

Using the conversion formulas $r=\sqrt{x^2+y^2}$ and $\theta=tan^{-1}\left ( y/x\right )$ ,

$r=\sqrt{x^2+y^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$

$\theta=tan^{-1}\left ( y/x\right )=tan^{-1}\left ( 12/5\right )=1.176$

The polar point is (13,1.176) .

Report an Error

Example Question #14 : Polar Calculations

Convert xy+7x^2=1+y into polar coordinates.

Possible Answers:

$r^2\left (sin\theta cos\theta+7cos^2\theta \right )=-1$

$r^2\left (sin\theta cos\theta+7sin^2\theta \right )-rcos\theta=7$

$r^2\left (sin\theta cos\theta+7cos^2\theta \right )-rsin\theta=1$

$rsin\theta=4$

Correct answer:

$r^2\left (sin\theta cos\theta+7cos^2\theta \right )-rsin\theta=1$

Explanation:

Substituting the conversion formulas $x=rcos\theta$ and $y=rsin\theta$ into the cartesian equation,

xy+7x^2=1+y

we get

$(rcos\theta)(rsin\theta)+7(rcos\theta)^2=1+(rsin\theta)$

$r^2sin\theta cos\theta+7r^2cos^2\theta=1+rsin\theta$

$r^2\left (sin\theta cos\theta+7cos^2\theta \right )-rsin\theta=1$

Report an Error

Example Question #21 : Polar Calculations

Convert 3x^2+3y^2=-4x into polar coordinates.

Possible Answers:

$r=\left (\frac{-4}{3} \right )sin\theta$

$r=\left (\frac{-4}{3} \right )cos\theta$

r=3

$r=-4cos^2\theta$

Correct answer:

$r=\left (\frac{-4}{3} \right )cos\theta$

Explanation:

Substituting the conversion formulas $x=rcos\theta$ and $y=rsin\theta$ into the cartesian equation,

3x^2+3y^2=-4x

we get

$3(rcos\theta)^2+3(rsin\theta)^2=-4rcos\theta$

$3r^2cos^2\theta+3r^2sin^2\theta=-4rcos\theta$

$3r^2(cos^2\theta+sin^2\theta)=-4rcos\theta$

Using the identity, $cos^2\theta+sin^2\theta=1$

$3r^2=-4rcos\theta$

$r=\left (\frac{-4}{3} \right )cos\theta$

Report an Error

Example Question #172 : Polar

Convert x^2+y^2=25 into polar coordinates.

Possible Answers:

$r=5cos\theta$

$r=5sin\theta cos\theta$

$r=5sin\theta$

r=5

Correct answer:

r=5

Explanation:

Substituting the conversion formulas $x=rcos\theta$ and $y=rsin\theta$ into the cartesian equation,

x^2+y^2=25

we get

$(rcos\theta)^2+(rsin\theta)^2=25$

$r^2cos^2\theta+r^2sin^2\theta=25$

$r^2(cos^2\theta+sin^2\theta)=25$

Using the identity, $cos^2\theta+sin^2\theta=1$

r^2=25

$r=\sqrt{25}=5$

Report an Error

Example Question #171 : Polar

Convert $r=4cos\theta$ into cartesian coordinates.

Possible Answers:

x^2+y^2=4x

x^2+4y^2=4x

x^2+y^2=4x+4y

x^2+y^2=4y

Correct answer:

x^2+y^2=4x

Explanation:

To make converting this expression easier, we will multiply both sides of the equation by , giving us

$r^2=4rcos\theta$

Substituting the conversion formulas r^2=x^2+y^2 and $x=rcos\theta$ into the polar equation, we get

x^2+y^2=4x

Report an Error

Example Question #174 : Polar

Convert $r=-7sin\theta$ into cartesian coordinates.

Possible Answers:

7x^2+7y^2=-y

x^2+y^2=-7y

x^2+y^2=x-y

x^2+y^2=-7x

Correct answer:

x^2+y^2=-7y

Explanation:

To make converting this expression easier, we will multiply both sides of the equation by , giving us

$r^2=-7rsin\theta$

Substituting the conversion formulas r^2=x^2+y^2 and $y=rsin\theta$ into the polar equation, we get

x^2+y^2=-7y

Report an Error

Example Question #21 : Polar Calculations

Convert $r=6cos\theta+2sin\theta$ into cartesian coordinates.

Possible Answers:

6x^2+2y^2=6x+2y

x^2+y^2=6x+2y

6x^2+y^2=x+2y

6x^2+2y^2=x-y

Correct answer:

x^2+y^2=6x+2y

Explanation:

To make converting this expression easier, we will multiply both sides of the equation by , giving us

$r^2=r(6cos\theta+2sin\theta)=6rcos\theta+2rsin\theta$

Substituting the conversion formulas r^2=x^2+y^2 , $x=rcos\theta$ and $y=rsin\theta$ into the polar equation, we get

x^2+y^2=6x+2y

Report an Error

Example Question #171 : Polar

Convert $\large \large \large (1,-1)$ into polar coordinates.

Possible Answers:

$\large \left ( 2, -\frac {\pi}{4}\right )$

$\large \left ( -2, \frac {\pi}{4}\right )$

$\large \left ( 2, \frac {\pi}{4}\right )$

$\large \left ( -2, -\frac {\pi}{4}\right )$

Correct answer:

$\large \left ( 2, -\frac {\pi}{4}\right )$

Explanation:

Screen shot 2016 01 02 at 10.52.46 am

Report an Error

View Calculus 2 Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

View Calculus 2 Tutors

Samita
Certified Tutor

University of Houston, Bachelor of Science, Computer Science. University of Houston, Non Degree Bachelors, Biology, General.

View Calculus 2 Tutors

Rohit K
Certified Tutor

Punjab Tech. University, Bachelor of Technology, Mechanical Engineering. Punjab Engineering College, Master of Engineering, M...

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in San Francisco-Bay Area, Physics Tutors in Atlanta, Computer Science Tutors in Seattle, GMAT Tutors in Atlanta, Computer Science Tutors in Los Angeles, Physics Tutors in Boston, Statistics Tutors in Houston, Physics Tutors in Philadelphia, Chemistry Tutors in Chicago, SSAT Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Chicago, GMAT Courses & Classes in Denver, SSAT Courses & Classes in Boston, Spanish Courses & Classes in Miami, ISEE Courses & Classes in Houston, Spanish Courses & Classes in Atlanta, MCAT Courses & Classes in Phoenix, MCAT Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in Philadelphia, GMAT Test Prep in Washington DC, LSAT Test Prep in Philadelphia, GMAT Test Prep in Seattle, ISEE Test Prep in Philadelphia, MCAT Test Prep in Los Angeles, MCAT Test Prep in Denver, GRE Test Prep in Seattle, SSAT Test Prep in Phoenix, ISEE 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

Calculus 2 : Polar

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #11 : Polar Calculations

Example Question #12 : Polar Calculations

Example Question #841 : Calculus Ii

Example Question #14 : Polar Calculations

Example Question #21 : Polar Calculations

Example Question #172 : Polar

Example Question #171 : Polar

Example Question #174 : Polar

Example Question #21 : Polar Calculations

Example Question #171 : Polar

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: