Can following trigonometric equation be simplified:

In summary, the conversation discusses simplifying the expression Fx = sin[90 - theta] * [dX - [tan(theta) * dY]]. It is determined that two trigonometric simplifications result in Fx = cos(theta) * dX - sin(theta) * dY. The variables in the equation are arbitrary.
  • #1
ireland01
17
0
Fx = sin [ 90 - theta ] * [ dX - [tan (theta) * dY ] ]

??
 
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  • #2
Do you mean
[tex]f(x)=\sin(90-\theta)[dX-(tan\theta)dY][/tex]
or what? I don't really understand what you wrote.
 
  • #3
sin(90- theta)= cos(theta) is one simplification.
 
  • #4
dalcde said:
Do you mean
[tex]f(x)=\sin(90-\theta)[dX-(tan\theta)dY][/tex]
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.
 
  • #5
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:

[tex]\mbox{Fx} = \cos(\theta) \, dX - \sin(\theta) \, dY[/tex]
 
  • #6
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:

[tex]\mbox{Fx} = \cos(\theta) \, dX - \sin(\theta) \, dY[/tex]

yeah. that's it. thanks.
 
  • #7
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.
 
  • #8
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.
 

FAQ: Can following trigonometric equation be simplified:

1. Can all trigonometric equations be simplified?

No, not all trigonometric equations can be simplified. Some equations may already be in their simplest form or may require more complex methods to simplify.

2. How do I know if a trigonometric equation can be simplified?

A trigonometric equation can usually be simplified if it contains trigonometric functions with similar arguments, such as sin(x) and cos(x), or if it can be rewritten in terms of a single trigonometric function.

3. What are some common trigonometric identities used for simplifying equations?

Some common trigonometric identities used for simplifying equations include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities.

4. Is there a specific order in which I should simplify a trigonometric equation?

There is no specific order in which a trigonometric equation should be simplified, but it may be helpful to follow the order of operations (PEMDAS) and simplify within parentheses first, then exponents, then multiplication and division, and finally addition and subtraction.

5. Are there any online tools or calculators that can simplify trigonometric equations?

Yes, there are many online tools and calculators available that can simplify trigonometric equations. Some popular options include WolframAlpha, Symbolab, and Mathway.

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