Really simple question, but I'm having trouble grasping this

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Homework Help Overview

The discussion revolves around understanding the area of a cardioid defined by the polar equation r = 2sinθ - 2, specifically focusing on the limits of integration for the first quadrant.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the choice of integration limits from π to 3π/2 for the first quadrant, suggesting that the first quadrant should be defined from 0 to π/2. Some participants explore the implications of negative or zero values of r in relation to the angle θ.

Discussion Status

The conversation indicates that there is some confusion regarding the definition of the first quadrant in this context. Participants are exploring different interpretations of the polar coordinates and their representation in the Cartesian plane. A suggestion to plot specific points has been made to aid understanding.

Contextual Notes

There appears to be a misunderstanding regarding the definition of quadrants in polar coordinates, particularly how negative values of r affect the representation of angles.

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Why is the area of the cardioid r = 2sinθ-2 in the first quadrant represented with limits from π to 3π/2 and not with limits from 0 to π/2? Isn't the first quadrant 0 to π/2?
 
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r is negative (or zero) for all values of theta, so when theta is between pi and 3 pi / 2, (r, theta) is in the first quadrant.
 
Actually, never mind, I'm still not understanding this :(
 
Last edited:
Try plotting the point for theta = 5 pi / 4. Maybe you will see it then.
 

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