Master Polar Coordinates: Solving for Distance Between A and B | Homework Help

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SUMMARY

The discussion focuses on solving for the distance between two points in polar coordinates, specifically (3a/2, π/3) and (-3a/2, -π/3). The user correctly identifies the polar coordinates and references the equation for distance, 2rSin(θ), as a method to calculate the distance between the two points. The conversation emphasizes the importance of determining whether to measure the straight-line distance or the arc length, suggesting a conversion to Cartesian coordinates using x = rcos(θ) and y = rsin(θ) for clarity in calculations.

PREREQUISITES
  • Understanding of polar coordinates and their representation
  • Familiarity with the equation for distance in polar coordinates: 2rSin(θ)
  • Basic knowledge of trigonometric functions and their applications
  • Ability to convert polar coordinates to Cartesian coordinates (x = rcos(θ), y = rsin(θ))
NEXT STEPS
  • Research the derivation and applications of the distance formula in polar coordinates
  • Learn about converting polar coordinates to Cartesian coordinates in depth
  • Explore trigonometric identities and their relevance in distance calculations
  • Study examples of distance calculations between points in polar coordinates
USEFUL FOR

Students studying mathematics, particularly those focusing on polar coordinates and trigonometry, as well as educators seeking to clarify concepts related to distance measurement in different coordinate systems.

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Homework Statement


CPT4011.jpg



Homework Equations





The Attempt at a Solution


a) I can get a quite easily:
theta = + and - pi/3

r = + and - 3a/2

b) Can someone guide me through how to get this. I want to find the distance between A and B
that is

(3a/2,pi/3), (-3a/2,-pi/3)

Thanks :)
 
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I still don't have a clue how to do part b. The mark scheme mentions using 2rSin(ө), is that the equation for measuring between two poitns? To find the distance do I want a straigh line between A and B or do I want to actually have an arc of length r and angle 2ө? Should I convert to cartesian form using x = rcos(ө) and y = rsin(x)

I don't have a clue :\

Thanks :)
 

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