Can Someone Explain This Trig Picture to Me?

  • Context: High School 
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    Explain Picture Trig
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Discussion Overview

The discussion revolves around understanding a trigonometric diagram related to the dot product and the angles involved in vector projections. Participants are trying to clarify the relationships between angles and the resulting trigonometric functions used in the calculations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about why the sine function is used in the context of the dot product, specifically questioning the transition from cosine to sine.
  • Another participant suggests that the diagram should be self-explanatory for those familiar with trigonometry.
  • A participant mentions the concept of projections onto different axes as a relevant aspect of the discussion.
  • One participant details their reasoning regarding the angles between vectors and the corresponding cosine values, but expresses uncertainty about the sign and value of the cosine for specific angles.
  • A later reply points out a specific part of the diagram, asserting that the dot product involving phi and y should yield a cosine function.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are conflicting interpretations of the angles and the resulting trigonometric functions. Some participants assert their understanding while others express confusion.

Contextual Notes

There are unresolved questions regarding the assumptions made about the angles and the definitions of the trigonometric functions in the context of the dot product. The discussion reflects varying levels of familiarity with trigonometric concepts.

Meadman23
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Its the attached picture. I'm not seeing why when using the dot product, they start using sin.
 

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The picture is self explanatory. If you know trig, it should be elementary.
 
Projections onto different axes.
 
I'm just not getting it. '
I see that the angle between r and x is phi, thus in using the formula, r (dot) x = (1)(1) cos(phi).

Then I see the angle between r and y is (90-phi), thus in using the formula, r (dot) y = (1)(1)cos(90-phi) = sin (phi).

I then see the angle between phi and x is (90 +phi), thus in using the formula, phi (dot) x = (1)(1)cos(90+phi) = -sin (phi)

I then see the angle between phi and y is (180 - phi), thus in using the formula, phi (dot) y = (1)(1)cos(180-phi) = -cos (phi)?

I don't get why the last one is +cos(phi)...
 
Look at the blue part of the diagram ... phi(dot)y = cos(phi).
 

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