We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus BC : AP Calculus BC

Study concepts, example questions & explanations for AP Calculus BC

Create An Account

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #171 : Parametric, Polar, And Vector

What is the equation $y=-\frac{1}{2}x^{2}$ in polar form?

Possible Answers:

$r=-2\tan \theta\sec\theta$

$r=2\tan \theta\sec\theta$

$r=-\tan 2\theta\sec\theta$

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

$r=-\frac{1}{2}\tan \theta\sec\theta$

Correct answer:

$r=-2\tan \theta\sec\theta$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given $y=-\frac{1}{2}x^{2}$ , then:

$r\sin\theta=-\frac{1}{2}(r\cos \theta)^{2}$

$r\sin\theta=-\frac{1}{2}r^{2}\cos^{2} \theta$

Dividing both sides by $r\cos\theta$ , we get:

$\tan \theta=-\frac{1}{2}r\cos\theta$

$\frac{\tan \theta}{\cos\theta}=-\frac{1}{2}r$

$\tan \theta\sec\theta=-\frac{1}{2}r$

$r=-2\tan \theta\sec\theta$

Report an Error

Example Question #1 : Polar Form

What is the polar form of $y=-7x^{2}$ ?

Possible Answers:

$r=-7\tan\theta\sec\theta$

$r=\frac{1}{7}\tan\theta\sec\theta$

$r=-\frac{1}{7}\tan\theta\sec\theta$

$r=\tan7\theta\sec\theta$

$r=7\tan\theta\sec\theta$

Correct answer:

$r=-\frac{1}{7}\tan\theta\sec\theta$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given $y=-7x^{2}$ , then:

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

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

Dividing both sides by $r\cos\theta$ , we get:

$\tan\theta=-7r\cos\theta$

$\frac{\tan\theta}{\cos\theta}=-7r$

$\tan\theta\sec\theta=-7r$

$r=-\frac{1}{7}\tan\theta\sec\theta$

Report an Error

Example Question #22 : Polar

What is the polar form of y=3-4x ?

Possible Answers:

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

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

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

None of the above

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

Correct answer:

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

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given y=3-4x , then:

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

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

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

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

Report an Error

Example Question #21 : Polar

What is the polar form of $y=-x^{2}$ ?

Possible Answers:

None of the above

$r=-\tan\theta\sec\theta$

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

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

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

Correct answer:

$r=-\tan\theta\sec\theta$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given $y=-x^{2}$ , then:

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

Dividing both sides by $r\cos\theta$ , we get:

$\tan\theta=-r\cos\theta$

$\frac{\tan\theta}{\cos\theta}=-r$

$\tan\theta\sec\theta=-r$

$r=-\tan\theta\sec\theta$

Report an Error

Example Question #23 : Polar

What is the polar form of y=-10x+5 ?

Possible Answers:

$r=\frac{5}{\sin\theta+10\cos\theta}$

None of the above

$r=-\frac{5}{\sin\theta-10\cos\theta}$

$r=\frac{5}{\sin\theta-10\cos\theta}$

$r=-\frac{5}{\sin\theta+10\cos\theta}$

Correct answer:

$r=\frac{5}{\sin\theta+10\cos\theta}$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given y=-10x+5 , then:

$r\sin\theta=-10(r\cos\theta)+5$

$r\sin\theta+10(r\cos\theta)=5$

$r(\sin\theta+10\cos\theta)=5$

$r=\frac{5}{\sin\theta+10\cos\theta}$

Report an Error

Example Question #24 : Polar

What is the polar form of $y=\frac{2}{3}x+9$ ?

Possible Answers:

$r=\frac{9}{\sin\theta-\frac{2}{3}\cos\theta}$

$r=-\frac{9}{\sin\theta+\frac{2}{3}\cos\theta}$

None of the above

$r=\frac{9}{\sin\theta+\frac{2}{3}\cos\theta}$

$r=-\frac{9}{\sin\theta-\frac{2}{3}\cos\theta}$

Correct answer:

$r=\frac{9}{\sin\theta-\frac{2}{3}\cos\theta}$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given $y=\frac{2}{3}x+9$ , then:

$r\sin\theta= \frac{2}{3}(r\cos\theta)+9$

$r\sin\theta-\frac{2}{3}(r\cos\theta)=9$

$r(\sin\theta-\frac{2}{3}\cos\theta)=9$

$r=\frac{9}{\sin\theta-\frac{2}{3}\cos\theta}$

Report an Error

Example Question #21 : Functions, Graphs, And Limits

What is the polar form of y=2x-7 ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given y=2x-7 , then:

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

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

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

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

Report an Error

Example Question #22 : Functions, Graphs, And Limits

What is the polar form of $y=\frac{3}{9}x^{2}$ ?

Possible Answers:

$r=3\tan \theta\sec\theta$

$r=-\frac{1}{3}\tan \theta\sec\theta$

$r=\frac{1}{3}\tan \theta\sec\theta$

$r=\tan \frac{1}{3}\theta\sec\theta$

$r=-3\tan \theta\sec\theta$

Correct answer:

$r=3\tan \theta\sec\theta$

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: $y=r\sin\theta$ and $x=r\cos\theta$ . Given $y=\frac{3}{9}x^{2}$ , then:

$r\sin\theta=\frac{3}9{}(r\cos \theta)^{2}$

$r\sin\theta=\frac{3}{9}r^{2}\cos^{2} \theta$

Dividing both sides by $r\cos\theta$ , we get:

$\tan \theta=\frac{3}9{}r\cos\theta$

$\frac{\tan \theta}{\cos\theta}=\frac{3}{9}r$

$\tan \theta\sec\theta=\frac{3}{9}r$

$r=\frac{9}{3}\tan \theta\sec\theta$

$r=3\tan \theta\sec\theta$

Report an Error

Example Question #23 : Functions, Graphs, And Limits

Convert the following cartesian coordinates into polar form: (-3,11)

Possible Answers:

$(\sqrt{130},74.74)$

$(\sqrt{130},-74.74)$

(8,74.74)

(8,-74.74)

Correct answer:

$(\sqrt{130},-74.74)$

Explanation:

Cartesian coordinates have x and y, represented as (x,y). Polar coordinates have $(r,\theta)$

is the hypotenuse, and $\theta$ is the angle.

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

$\theta = \arctan(\frac{y}{x})$

Solution:

x=-3

y=11

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

$r = \sqrt{(-3)^2+11^2 }= \sqrt{(9+121)}$

$r = \sqrt{130}$

$\theta = \arctan(\frac{y}{x})$

$\theta = \arctan(-\frac{11}{3}) = -74.74$

$(\sqrt{130},-74.74)$

Report an Error

Example Question #24 : Functions, Graphs, And Limits

Convert the following cartesian coordinates into polar form: (6,-14)

Possible Answers:

$(\sqrt{232},-66.8)$

$(\sqrt{210},-42.8)$

$(\sqrt{225},54.8)$

$(\sqrt{230},62.8)$

Correct answer:

$(\sqrt{232},-66.8)$

Explanation:

Cartesian coordinates have x and y, represented as (x,y). Polar coordinates have $(r,\theta)$

is the hypotenuse, and $\theta$ is the angle.

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

$\theta = \arctan(\frac{y}{x})$

Solution:

x=6

y=-14

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

$r=\sqrt{(6)^2 + (-14)^2}$

$r=\sqrt{36+196}$

$r=\sqrt{232}$

$\theta=\arctan(\frac{y}{x})$

$\theta=\arctan(\frac{-14}{6})$

$\theta=-66.8$

$(\sqrt{232},-66.8)$

Report an Error

View AP Calculus BC Tutors

Woo
Certified Tutor

Sungkyunkwan University in Seoul Korea, Bachelor of Engineering, Metallurgical Engineering.

View AP Calculus BC Tutors

Benjamin
Certified Tutor

Portland State University, Bachelor of Science, Computer Science.

View AP Calculus BC Tutors

Mohammed
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Electrical Engineering. University of Maryland-College Park, Master...

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Philadelphia, French Tutors in Washington DC, Chemistry Tutors in Miami, Computer Science Tutors in Washington DC, Computer Science Tutors in New York City, Biology Tutors in Dallas Fort Worth, Algebra Tutors in Dallas Fort Worth, Physics Tutors in Miami, Physics Tutors in Phoenix, Physics Tutors in Chicago

Popular Courses & Classes

GRE Courses & Classes in Boston, SAT Courses & Classes in Houston, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Chicago, SAT Courses & Classes in Atlanta, LSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in San Diego, ACT Test Prep in New York City, GMAT Test Prep in Chicago, SAT Test Prep in Chicago, ISEE Test Prep in San Diego, LSAT Test Prep in San Diego, LSAT Test Prep in Seattle, MCAT Test Prep in Chicago, SSAT Test Prep in Phoenix, GMAT Test Prep in Dallas Fort Worth

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

AP Calculus BC : AP Calculus BC

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

Example Questions

Example Question #171 : Parametric, Polar, And Vector

Example Question #1 : Polar Form

Example Question #22 : Polar

Example Question #21 : Polar

Example Question #23 : Polar

Example Question #24 : Polar

Example Question #21 : Functions, Graphs, And Limits

Example Question #22 : Functions, Graphs, And Limits

Example Question #23 : Functions, Graphs, And Limits

Example Question #24 : Functions, Graphs, And Limits

All AP Calculus BC Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: