Are these the correct cos and sin relations for the given values?

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Discussion Overview

The discussion revolves around the correctness of trigonometric relations involving cosine and sine for given angles, specifically in the context of a mathematical equation that combines these functions. The scope includes mathematical reasoning and verification of identities.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a relationship involving cosines and sines of angles and questions its correctness.
  • Another participant raises the issue of the sign of sine, suggesting that if one of the sine values is negative, it could affect the overall equation.
  • A third participant clarifies the ranges of the angles involved, asserting that sine will always be positive within those ranges but questions if the two equations are equal.
  • Several questions are posed regarding the variables involved, including whether \theta and \Theta are the same and the meaning of \phi, indicating a need for more context.
  • One participant affirms that the final relationship follows from the initial equations presented.
  • A later reply expresses relief at the validation of their reasoning, indicating a desire for confirmation of their understanding.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correctness of the equations, with some affirming the relationship while others question specific aspects and seek clarification. The discussion remains unresolved on certain points, particularly regarding the implications of sine values and the definitions of variables.

Contextual Notes

There are limitations in the clarity of variable definitions and the context of the equations presented, which may affect the interpretation of the relationships discussed.

Somefantastik
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if

\mu = cos(\theta) and \mu_{0} = cos(\theta_{0})

and

cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi)

Then

cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi)


Is this not correct?
 
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Somefantastik said:
Is this not correct?

What if one of the sines is negative?
 
sorry, range of \theta is 0 to 60 degrees, and \theta_{0} range is 0 to 70 degrees. As far as I can tell, sin will always be positive. But regardless, sin(theta)< 0 would change the value of the over all equation, but are the two equations not equal?
 
Several questions:

(1) Are \theta and \Theta the same variable?

(2) What is \phi?

(3) I'm not sure what the equation is getting at. It appears to be a hyrid of a cofunction, symmetric, and angle sum identity. Something feels missing. Could you provide more detail as to what you are trying to show here?

--Elucidus
 
Yes, your final relationship follows from what you have given.
 
Ok thanks Integral; I just wanted to make sure I wasn't crazy
 

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