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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)
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°.
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### 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.
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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