9. Convert the following rectangular point to polar form: (-2,2√3) 10. Convert the following polar point to rectangular form: (-2,-7π/6)
9. Convert the following rectangular point to polar form: (-2,2√3) 10. Convert the following polar point to rectangular form: (-2,-7π/6)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Coordinate Conversion Problems
Below are a set of problems related to converting between rectangular and polar coordinates.
#### Problem 9
Convert the following rectangular point to polar form: \((-2, 2\sqrt{3})\).
Solution:
Rectangular coordinates \((x, y)\) can be converted to polar coordinates \((r, \theta)\) using the following formulas:
- \( r = \sqrt{x^2 + y^2} \)
- \( \theta = \tan^{-1}\left(\frac{y}{x}\right) \)
#### Problem 10
Convert the following polar point to rectangular form: \((-2, -\frac{7\pi}{6})\).
Solution:
Polar coordinates \((r, \theta)\) can be converted to rectangular coordinates \((x, y)\) using the following formulas:
- \( x = r \cos(\theta) \)
- \( y = r \sin(\theta) \)
These exercises help in understanding the relationship between rectangular (Cartesian) coordinates and polar coordinates, which are commonly used in fields such as physics, engineering, and navigation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd88595c7-c499-4476-ae94-4573188e2c46%2Faa422647-e428-47a7-afbb-c16425349b13%2Fpjhy7pb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Coordinate Conversion Problems
Below are a set of problems related to converting between rectangular and polar coordinates.
#### Problem 9
Convert the following rectangular point to polar form: \((-2, 2\sqrt{3})\).
Solution:
Rectangular coordinates \((x, y)\) can be converted to polar coordinates \((r, \theta)\) using the following formulas:
- \( r = \sqrt{x^2 + y^2} \)
- \( \theta = \tan^{-1}\left(\frac{y}{x}\right) \)
#### Problem 10
Convert the following polar point to rectangular form: \((-2, -\frac{7\pi}{6})\).
Solution:
Polar coordinates \((r, \theta)\) can be converted to rectangular coordinates \((x, y)\) using the following formulas:
- \( x = r \cos(\theta) \)
- \( y = r \sin(\theta) \)
These exercises help in understanding the relationship between rectangular (Cartesian) coordinates and polar coordinates, which are commonly used in fields such as physics, engineering, and navigation.
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