Why is z = rcos(θ) and not z = rsin(θ) in surface integrals?

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Homework Help Overview

The discussion revolves around the use of polar coordinates in surface integrals, specifically addressing why the relationship z = rcos(θ) is preferred over z = rsin(θ). Participants are exploring the geometric interpretations and symmetry involved in these equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the symmetry between the variables x and z and whether it affects the choice of cosine or sine in the equations. Some express confusion over differing results when using sine instead of cosine.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the symmetry of the setup and its implications. There is acknowledgment of differing answers based on the choice of trigonometric functions, but no consensus has been reached on the preferred approach.

Contextual Notes

Some participants mention having different outcomes when using sine, indicating potential misunderstandings or assumptions that may need clarification. The symmetry of the setup is a recurring theme in the discussion.

Miike012
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Look in the paint doc. I was wondering why they said z = rcos(θ) and not z = rsin(θ) and x = rcos(θ)
 

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The set-up is symmetric between x and z, so does it matter which is equated with the cos and which with the sin?
 
haruspex said:
The set-up is symmetric between x and z, so does it matter which is equated with the cos and which with the sin?

Well when i used sine I came out with a different answer but ill try again.
 
haruspex said:
The set-up is symmetric between x and z, so does it matter which is equated with the cos and which with the sin?

You are right the answers are the same. thanks.
 

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