Can following trigonometric equation be simplified:

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Discussion Overview

The discussion revolves around the simplification of a trigonometric equation involving the sine and tangent functions. Participants explore whether the expression can be simplified and clarify the components of the equation.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the equation Fx = sin [ 90 - theta ] * [ dX - [tan (theta) * dY ] ] and seeks simplification.
  • Another participant questions the notation and expresses confusion about the equation's structure.
  • A participant suggests that sin(90 - theta) can be simplified to cos(theta), indicating a potential simplification.
  • Further clarification is provided that the left side of the equation is not being simplified, but rather the right side is being addressed.
  • Another participant confirms that the simplification leads to Fx = cos(theta) * dX - sin(theta) * dY, acknowledging the simplification process.
  • There is a correction regarding which side of the equation was simplified, with participants confirming the right side was the focus.

Areas of Agreement / Disagreement

Participants generally agree that the equation can be simplified, but there is some confusion regarding the notation and which side of the equation is being simplified. The discussion remains somewhat unresolved regarding the clarity of the initial expression.

Contextual Notes

There are limitations in understanding the definitions of Fx, dX, and dY, which may affect the interpretation of the simplifications discussed.

ireland01
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Fx = sin [ 90 - theta ] * [ dX - [tan (theta) * dY ] ]

??
 
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Do you mean
f(x)=\sin(90-\theta)[dX-(tan\theta)dY]
or what? I don't really understand what you wrote.
 
sin(90- theta)= cos(theta) is one simplification.
 
dalcde said:
Do you mean
f(x)=\sin(90-\theta)[dX-(tan\theta)dY]
or what? I don't really understand what you wrote.

Yes. I mean variables are arbitrary. I just want to know if the left side of the eqn can be simplified at all.
 
Without trying to interpret exactly what Fx, dX or dY denote the simple answer is yes, there are two obvious trigonometric simplifications that result in:

\mbox{Fx} = \cos(\theta) \, dX - \sin(\theta) \, dY
 
uart said:
Without trying to interpret exactly what Fx, dX or dY denote the simple answer is yes, there are two obvious trigonometric simplifications that result in:

\mbox{Fx} = \cos(\theta) \, dX - \sin(\theta) \, dY

yeah. that's it. thanks.
 
ireland01 said:
Yes. I mean variables are arbitrary. I just want to know if the left side of the eqn can be simplified at all.
And, by the way, it was the right side of the equation that was simplified, not the left side.
 
HallsofIvy said:
And, by the way, it was the right side of the equation that was simplified, not the left side.

yes. thanks. corrected above.
 

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