
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
![Suppose that \( P = (x, y) \) has polar coordinates \(\left( r, \frac{\pi}{15} \right)\). Find the polar coordinates for the following points if \( \theta \in [0, 2\pi] \).
(a) \( P = (x, -y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*
(b) \( P = (-x, -y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, \pi \right) \]
*Incorrect*
(c) \( P = (-x, y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*
(d) \( P = (y, x) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*](https://content.bartleby.com/qna-images/question/c9b629bd-7b7c-4b52-85cc-46a95271ddc8/07d22e01-87e9-4b1e-a3e8-d4bce75d9ea5/i09ue7_thumbnail.png)
Transcribed Image Text:Suppose that \( P = (x, y) \) has polar coordinates \(\left( r, \frac{\pi}{15} \right)\). Find the polar coordinates for the following points if \( \theta \in [0, 2\pi] \).
(a) \( P = (x, -y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*
(b) \( P = (-x, -y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, \pi \right) \]
*Incorrect*
(c) \( P = (-x, y) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*
(d) \( P = (y, x) \)
(Give your answer in the form \((*, *)\). Express numbers in exact form. Use symbolic notation and fractions where needed.)
**Polar coordinates:**
\[ \left( \sqrt{x^2 + y^2}, 0 \right) \]
*Incorrect*
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps

Knowledge Booster
Similar questions
- Choose the point which shows the correct location for the polar coordinate (-2,-). 元 90° 120 WIN 135° 45° 1 -7 radians 150° 30° 57 15° C 3 radians- 12 180° 0°27 360° E Low Disk S We need m updates. Sel 6 radians 330° 11 210° 315 25° O Type here to search R. PIDEJ 2 radians.arrow_forward14. (a) Given the point (2, 150°) in polar coordinates, find a corresponding point in rectangular coordinates. (State exact values, not decimal approximations.) Answer: (b) Given the point (-8,– 8) in rectangular coordinates, find a corresponding point in polar coordinates. Express the angle exactly in radians. (Your angle should include Tt). Answer:arrow_forwardCannot solvearrow_forward
- Graph each polar equation given below. (a) r sin e = -3 (b) r=5 Part (a) 21 Part (b) 21 e to 2 3 31 3n 4 十 + 9. 图 4 11m 111 Submi Continue © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy CenterA Fle Elmarrow_forwardFor 10.3, we would like to understand some basic idea of polar coordinate and polar equations: 57 3) Plot the points with polar coordinates: (3, ), (– 4, –5), (– 2, 7), (5, –), (1, – 4). 4 rewrite each polar coordinate in another way, where r is the opposite of the original value and theta is between O and 2pi. For example: (3, ) = (- 3,0), 0<0 < 2m 6.arrow_forwardConvert the polar point (2, 27/3) to an equivalent polar point where r < 0 and 0 <0 < 2n. OA. (2, —4т /3) Ов. (-2, 5л /3) OC. (-2, 7/3) OD. (-2,4л/3) O E (-2, –7/3) O F. (-2, 11т/3)arrow_forward
- (1) =j. Listen Perform the indicated operations and express the result in the requested form. (35e0.371) (5.98e1.661); express in polar form 209.3/116.31° 40.98/116.31° 209.3/2.03° 209.3/58.16° Previous Page -1)=-j. exponent. Next Page Ost Page 25 of 30arrow_forwardThe first part of this problem lists Polar Coordinates for six points. Match each Polar coordinate (r, 0) with the equivalent Rectangular coordinates (x.y). Don't use a calculator. 1. 11 2. 137 3. (8, 6 27 4. (8 2 5. (8, -57 6, 亭) 6. A. (4V2, 4v2) B. (4/3, 4) C. (3,3/3) D. (4v3, -4) E. (-8,0) F. (4/2, 4/2)arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning