Solving for Spherical Coordinate Angles in 3D: Understanding the Formulas

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Discussion Overview

The discussion revolves around understanding the formulas for spherical coordinates in three dimensions, specifically focusing on the derivation and application of the equations for calculating the components of a vector in spherical coordinates.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the spherical coordinate formulas, particularly why the Z-axis component uses only cosine while the X and Y components involve both sine and cosine.
  • Another participant suggests that understanding can be enhanced by exploring right triangles and recommends looking for geometric explanations online.
  • A later reply offers a diagram as a potential aid in understanding the concepts discussed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the explanation of the formulas, and the discussion includes varying levels of understanding and clarity regarding the geometric interpretation of the spherical coordinates.

Contextual Notes

The discussion lacks detailed geometric representations and assumes familiarity with the concepts of spherical coordinates and trigonometric functions, which may limit understanding for some participants.

ricky_fusion
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Hi guys,
This is my first time in this forum, thanks for your time.
Now, I learn about spherical angles (vektor) in 3 Dimension
I still confuse about the formula, such as:
Fx = F sinφ cosθ ( in X axis = i)
Fy = F sinφ sinθ ( in y-axis = j)
Fz = F cosφ ( in z axis = k)

I want to send the pictures too, but I still don't have the way to upload it.Maybe next time.
Does anybody know about why in X axis there are sin and cos but in Z axis there is only cos??
Thaks for your help.
 
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You can calculate all these by playing around with right triangles... I only just learned this stuff 2 weeks ago, so I can hardly explain it in words. I would look around online for a detailed picture that explains how the equations are geometrically derived. it isn't too complicated.
 
Does this diagram help?
 

Attachments

  • spherical-coords.gif
    spherical-coords.gif
    30.1 KB · Views: 667
Hmm..
Yes, you are right, Thanks a lot.
 

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