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

← Previous 1 2 3 4 5 6 Next →

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert from polar form to rectangular form:

$r=4\cos\theta$

Possible Answers:

x^2+y^2+4=0

(x+y)^2=4

(x-2)^2+y^2=4

(x+2)^2+y^2=4

Correct answer:

(x-2)^2+y^2=4

Explanation:

Start by multiplying both sides by .

$r=4\cos\theta$

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

Keep in mind that r^2=x^2+y^2

$x^2+y^2=4r\cos\theta$

Remember that $x=r\cos\theta$

So then,

x^2+y^2=4x

x^2-4x+y^2=0

Now, complete the square.

(x^2-4x+4)+y^2=4

(x-2)^2+y^2=4

Report an Error

Example Question #3 : Polar Coordinates

Convert the polar equation to rectangular form:

$r=8\sin\theta$

Possible Answers:

x^2+(y+4)^2=16

x^2+(y-4)^2=16

(x-4)^2+y^2=15

(x+y-4)^2=16

Correct answer:

x^2+(y-4)^2=16

Explanation:

Start by multiplying both sides by .

$r=8\sin\theta$

$r^2=8r\sin\theta$

Remember that r^2=x^2+y^2

$x^2+y^2=8r\sin\theta$

Keep in mind that $y=r\sin\theta$

So then,

x^2+y^2=8y

x^2+y^2-8x=0

Now, complete the square.

x^2+(y^2-8x+16)=16

x^2+(y-4)^2=16

This is a graph of a circle with a radius of and a center at (0, 4)

Report an Error

Example Question #4 : Polar Coordinates

Convert the polar equation into rectangular form:

$r=8\sec\theta$

Possible Answers:

x^2+y^2=8

(x-1)^2+y^2=64

y=8

x=8

Correct answer:

x=8

Explanation:

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

So then $r=8\sec\theta$ becomes

$r=\frac{8}{\cos\theta}$

Now, multiply both sides by $\cos\theta$ to get rid of the fraction.

$r\cos\theta=8$

Since $x=r\cos\theta,$ the rectangular form of this equation is

x=8

Report an Error

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

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

Possible Answers:

(x^2+y^2+8)=16

(x^2+y^2)^2=8xy

(x^2+y^2)^2=8

(x^2-^2)^2=8xy

Correct answer:

(x^2+y^2)^2=8xy

Explanation:

Start by using the double angle formula for $\sin$ .

$\sin(2\theta)=2\sin\theta\cos\theta$

Substitute that into the equation gives the following:

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

$r^2=8\sin\theta\cos\theta$

Because we need $r\cos\theta$ and $r\sin\theta$ to get and respectively, multiply both sides by r^2 .

$(r^2)(r^2)=8(r\sin\theta)(r\cos\theta)$

Now, recall that r^2=x^2+y^2 .

(x^2+y^2)(x^2+y^2)=8xy

(x^2+y^2)^2=8xy

Report an Error

Example Question #6 : Polar Coordinates

Convert the polar equation to rectangular form:

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

Possible Answers:

$y=-\frac{\sqrt3}{3}x$

$y=-\sqrt3x$

$y=-\frac{3}\sqrt3}x$

y=-3x

Correct answer:

$y=-\frac{\sqrt3}{3}x$

Explanation:

Start by taking the tangent.

$\tan\theta=\tan\frac{5\pi}{6}$

$\tan\theta=-\frac{\sqrt3}{3}$

Recall that $\tan\theta=\frac{y}{x}$

$\frac{y}{x}=-\frac{\sqrt3}{3}$

$y=-\frac{\sqrt3}{3}x$

Report an Error

Example Question #7 : Polar Coordinates

Convert the polar equation to rectangular form:

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

Possible Answers:

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

y=-x

y=x

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

Correct answer:

y=x

Explanation:

Start by taking the tangent.

$\tan\theta=\tan\frac{5\pi}{4}$

$\tan\theta=1$

Recall that $\tan\theta=\frac{y}{x}$

$\frac{y}{x}=1$

y=x

Report an Error

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

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

Possible Answers:

$y=2\sqrt x$

$y=\frac{1}{2}x^2$

x=4y^2

$y=\frac{1}{4}x^2$

Correct answer:

$y=\frac{1}{4}x^2$

Explanation:

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

Substituting this into the given equation gives

$r=4\frac{1}{\cos\theta}\tan\theta$

Multiply both sides by $\cos\theta$ to get rid of the fraction.

$r\cos\theta=4\tan\theta$

Recall that $x=r\cos\theta$ and that $\tan\theta=\frac{y}{x}$

$x=4\frac{y}{x}$

4y=x^2

$y=\frac{1}{4}x^2$

Report an Error

Example Question #9 : Polar Coordinates

Convert the polar equation into rectangular form:

$r=2\csc\theta\cot\theta$

Possible Answers:

$y=\sqrt{2x}$

$y=\sqrt{\frac{x}{2}}$

$y=-\sqrt{2x}$

y=2x^2

Correct answer:

$y=\sqrt{2x}$

Explanation:

Recall that $\csc\theta=\frac{1}{sin\theta}$ and $\cot\theta=\frac{1}{tan\theta}$

$r=2\frac{1}{\sin\theta}\frac{1}{\tan\theta}$

Multiply both sides by $\sin\theta$

$r\sin\theta=2(\frac{1}{\tan\theta})$

Recall that $\tan\theta=\frac{y}{x}$ and $r\sin\theta=y$

$y=2(\frac{1}{\frac{y}{x}})$

$y=2(\frac{x}{y})$

2x=y^2

$y=\sqrt{2x}$

Report an Error

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

$r=-3\sec\theta$

Possible Answers:

y=-3

x^2+y^2=-3

x=-3

(x-3)^2=4

Correct answer:

x=-3

Explanation:

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

Plugging this into the equation gives us

$r=-3\frac{1}{\cos\theta}$

Multiply both sides by $\cos\theta$ to get rid of the fraction.

$r\cos\theta=-3$

Recall that $r\cos\theta=x$

So then the rectangular form of the equation is x=-3

Report an Error

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form.

$6r=\csc\theta$

Possible Answers:

y=6

$x=\frac{1}{6}$

y^2=6

$y=\frac{1}{6}$

Correct answer:

$y=\frac{1}{6}$

Explanation:

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

$6r=\frac{1}{\sin\theta}$

Multiply both sides by $\sin\theta$ to get rid of the fraction.

$6r\sin\theta=1$

Recall that $y=r\sin\theta$ .

6y=1

$y=\frac{1}{6}$

Report an Error

← Previous 1 2 3 4 5 6 Next →

View Pre-Calculus Tutors

Michael
Certified Tutor

University of Ghana Legon, Bachelor in Arts, Statistics. University of Louisiana-Monroe, Non Degree Bachelors, Education.

View Pre-Calculus Tutors

Antoine
Certified Tutor

University of West Georgia, Bachelor of Science, Mathematics. University of West Georgia, Master of Arts, Mathematics Teacher...

View Pre-Calculus Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

All Precalculus Resources

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

Popular Subjects

Biology Tutors in Miami, Math Tutors in Denver, Reading Tutors in New York City, SAT Tutors in Washington DC, MCAT Tutors in Boston, Algebra Tutors in Denver, SSAT Tutors in Los Angeles, Statistics Tutors in Phoenix, Reading Tutors in Seattle, Reading Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in Houston, SAT Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, GMAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Atlanta, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Miami, ISEE Courses & Classes in Houston, MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SSAT Test Prep in Chicago, ISEE Test Prep in Boston, MCAT Test Prep in Los Angeles, LSAT Test Prep in Miami, GMAT Test Prep in Phoenix, SSAT Test Prep in Washington DC, GMAT Test Prep in Los Angeles, ACT Test Prep in Atlanta, MCAT Test Prep in Houston, SSAT 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

Precalculus : Convert Polar Equations To Rectangular Form and vice versa

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #3 : Polar Coordinates

Example Question #4 : Polar Coordinates

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #6 : Polar Coordinates

Example Question #7 : Polar Coordinates

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #9 : Polar Coordinates

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: