Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Convert Polar Equations To Rectangular Form and vice versa

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 #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation into polar form.

y=3x+2

Possible Answers:

$r=\frac{\sin\theta-3\cos\theta}{2}$

$r=\sin\theta-3\cos\theta$

$r=2(\sin\theta-3\cos\theta)$

$r=\frac{2}{\sin\theta-3\cos\theta}$

Correct answer:

$r=\frac{2}{\sin\theta-3\cos\theta}$

Explanation:

Recall that $x=r\cos\theta$ and $y=r\sin\theta$ .

Substitute these values into the equation.

$r\sin\theta=3(r\cos\theta)+2$

Now, manipulate the equation so that the terms with are on the same side.

$r\sin\theta-3r\cos\theta=2$

Factor out the .

$r(\sin\theta-3\cos\theta)=2$

Divide both sides by $\sin\theta-3\cos\theta$ .

$r=\frac{2}{\sin\theta-3\cos\theta}$

Report an Error

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Conver the rectanglar equation into polar form.

y=-2x-5

Possible Answers:

$r=-\frac{5}{\sin\theta+2\cos\theta}$

$r=-2\cos\theta-\sin\theta$

$r=-5(\sin\theta+2\cos\theta)$

$r=-\frac{\sin\theta+2\cos\theta}{5}$

Correct answer:

$r=-\frac{5}{\sin\theta+2\cos\theta}$

Explanation:

Recall that $x=r\cos\theta$ and $y=r\sin\theta$ .

Substitute these values into the equation.

$r\sin\theta=-2(r\cos\theta)-5$

Now, manipulate the equation so that the terms with are on the same side.

$r\sin\theta+2r\cos\theta=-5$

Factor out the .

$r(\sin\theta+2\cos\theta)=-5$

Divide both sides by $\sin\theta+2\cos\theta$ .

$r=-\frac{5}{\sin\theta+2\cos\theta}$

Report an Error

Example Question #102 : Polar Coordinates And Complex Numbers

Convert the rectangular equation to polar form.

x=7y+2

Possible Answers:

$r=2(\cos\theta-7\sin\theta)$

$r=\frac{\cos\theta-7\sin\theta}{2}$

$r=\frac{2}{\sin\theta-7\cos\theta}$

$r=\frac{2}{\cos\theta-7\sin\theta}$

Correct answer:

$r=\frac{2}{\cos\theta-7\sin\theta}$

Explanation:

Recall that $x=r\cos\theta$ and $y=r\sin\theta$ .

Substitute these values into the equation.

$r\cos\theta=7(r\sin\theta)+2$

Now, manipulate the equation so that the terms with are on the same side.

$r\cos\theta-7r\sin\theta=2$

Factor out the .

$r(\cos\theta-7\sin\theta)=2$

Divide both sides by $\cos\theta-7\sin\theta$ .

$r=\frac{2}{\cos\theta-7\sin\theta}$

Report an Error

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form.

x=-3y-4

Possible Answers:

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

$r=-\frac{4}{\sin\theta+3\cos\theta}$

$r=-\frac{\cos\theta+3\sin\theta}{4}$

$r=-\frac{4}{\cos\theta+3\sin\theta}$

Correct answer:

$r=-\frac{4}{\cos\theta+3\sin\theta}$

Explanation:

Recall that $x=r\cos\theta$ and $y=r\sin\theta$ .

Substitute these values into the equation.

$r\cos\theta=-3(r\sin\theta)-4$

Now, manipulate the equation so that the terms with are on the same side.

$r\cos\theta+3r\sin\theta=-4$

Factor out the .

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

Divide both sides by $\cos\theta+3\sin\theta$ .

$r=-\frac{4}{\cos\theta+3\sin\theta}$

Report an Error

Example Question #36 : Polar Coordinates

Convert from rectangular form to polar.

y^2=3y-x^2

Possible Answers:

$r=3\sin\theta$

$r=3\cos^2\theta$

$r=\frac{3}{\sin^2\theta}$

$r=3\sin\theta\cos\theta$

Correct answer:

$r=3\sin\theta$

Explanation:

Recall that $y=r\sin\theta$ and $x=r\cos\theta$ .

Substitute those into the equation.

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

Expand the equation.

$r^2\sin^2\theta=3\sin\theta-r^2\cos^2\theta$

Add $r^2\cos^2\theta$ to both sides.

$r^2\sin^2\theta+r^2\cos^2\theta=3r\sin\theta$

Factor out r^2 .

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

Remember that $\sin^2\theta+\cos^2\theta=1$ .

$r^2=3r\sin\theta$

Divide both sides by .

$r=3\sin\theta$

Report an Error

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form.

x^2-6x+y^2=0

Possible Answers:

$r=6\sin\theta$

$r=\frac{6}{\cos^2\theta}$

$r=6\cos\theta$

$r=6\cos^2\theta\sin\theta$

Correct answer:

$r=6\cos\theta$

Explanation:

Recall that $y=r\sin\theta$ and $x=r\cos\theta$ .

Substitute those into the equation.

$(r\cos\theta)^2-6(r\cos\theta)+(r\sin\theta)^2=0$

Expand this equation.

$r^2\cos^2\theta+r^2\sin^2\theta-6r\cos\theta=0$

Add $6r\cos\theta$ to both sides.

$r^2\cos^2\theta+r^2\sin^2\theta=6r\cos\theta$

Factor out r^2 on the left side of the equation.

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

Recall that $\sin^2\theta+\cos^2\theta=1$

$r^2=6r\cos\theta$

Divide both sides by .

$r=6\cos\theta$

Report an Error

Example Question #34 : Polar Coordinates

Convert the rectangular equation into polar form.

y=4x^2

Possible Answers:

$r=\frac{4}{\tan\theta\sec\theta}$

$r=\frac{\tan\theta\sec\theta}{4}$

$r=\frac{\cot\theta\sec\theta}{4}$

$r=4(\tan\theta\sec\theta)$

Correct answer:

$r=\frac{\tan\theta\sec\theta}{4}$

Explanation:

Recall that $y=r\sin\theta$ and $x=r\cos\theta$ .

Substitute those into the equation.

$r\sin\theta=4(r\cos\theta)^2$

Expand this equation.

$r\sin\theta=4r^2\cos^2\theta$

Subtract both sides by $r\sin\theta$ .

$4r^2\cos^2\theta-r\sin\theta=0$

Factor out the .

$r(4r\cos^2\theta-\sin\theta)=0$

At this point, either r=0 or $4r\cos^2\theta-\sin\theta=0$ . Let's continue solving the latter equation to get a more meaningful answer.

$4r\cos^2\theta-\sin\theta=0$

Add $\sin\theta$ to both sides.

$4r\cos^2\theta=\sin\theta$

Divide both sides by $4\cos^2\theta$ to solve for .

$r=\frac{\sin\theta}{4\cos^2\theta}$

Recall that $tan\theta=\frac{\sin\theta}{\cos\theta}$ and that $\frac{1}{\cos\theta}=\sec\theta$ .

$r=\frac{\tan\theta\sec\theta}{4}$

Report an Error

Example Question #32 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form:

x=9

Possible Answers:

$r=9\sec\theta$

$r=9\cos\theta$

$r=9\csc\theta$

$r=9\sin\theta$

Correct answer:

$r=9\sec\theta$

Explanation:

Recall that $x=r\cos\theta$

Substitute that into the equation.

$r\cos\theta=9$

Recall that,

$\frac{1}{\cos\theta}=\sec\theta$

$r=\frac{9}{\cos\theta}=9\sec\theta$

Report an Error

Example Question #40 : Polar Coordinates

Convert the rectangular equation to polar form:

x=-5

Possible Answers:

$r=-5\sec\theta$

$r=-5\cos\theta$

$r=-5\csc\theta$

$r=-5\sin\theta$

Correct answer:

$r=-5\sec\theta$

Explanation:

Recall that $x=r\cos\theta$ .

Substitute that into the equation.

$r\sin\theta=-5$

Now, isolate the on one side.

$r=\frac{-5}{\sin\theta}$

Recall that,

$\frac{1}{\cos\theta}=\sec\theta$

$r=-5\sec\theta$

Report an Error

Example Question #105 : Polar Coordinates And Complex Numbers

Convert the rectangular equation into polar form.

y=2

Possible Answers:

$r=2\sec\theta$

$r=\cos\theta$

$r=2\sin\theta$

$r=2\csc\theta$

Correct answer:

$r=2\csc\theta$

Explanation:

Recall that $y=r\sin\theta$

Substitute that into the equation.

$r\sin\theta=2$

Recall that,

$\frac{1}{\sin\theta}=\csc\theta$

$r=\frac{2}{\sin\theta}=2\csc\theta$

Report an Error

View Pre-Calculus Tutors

Tracy
Certified Tutor

Clarion University of Pennsylvania, Bachelor of Science, Physics.

View Pre-Calculus Tutors

Yaakoub
Certified Tutor

CUNY Queens College, Bachelor of Science, Finance. Vaughn College of Aeronautics and Technology, Bachelor of Science, Electri...

View Pre-Calculus Tutors

Emmanuel
Certified Tutor

Baylor University, Bachelor of Science, Biology, General.

All Precalculus Resources

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

Popular Subjects

MCAT Tutors in Boston, Chemistry Tutors in San Francisco-Bay Area, GRE Tutors in Los Angeles, LSAT Tutors in Houston, Computer Science Tutors in San Francisco-Bay Area, Spanish Tutors in Dallas Fort Worth, Math Tutors in Boston, Spanish Tutors in Atlanta, ACT Tutors in Washington DC, Statistics Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Atlanta, ACT Courses & Classes in Miami, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in New York City, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Boston, GRE Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Miami, GMAT Test Prep in Denver, ACT Test Prep in Miami, SSAT Test Prep in Denver, SAT Test Prep in Miami, MCAT Test Prep in Phoenix, ACT Test Prep in Denver, GMAT Test Prep in Washington DC

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 : Convert Polar Equations To Rectangular Form and vice versa

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #102 : Polar Coordinates And Complex Numbers

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #36 : Polar Coordinates

Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #34 : Polar Coordinates

Example Question #32 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #40 : Polar Coordinates

Example Question #105 : Polar Coordinates And Complex Numbers

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: