- #1

ireland01

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

??

??

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- Thread starter ireland01
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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

dalcde

- 166

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[tex]f(x)=\sin(90-\theta)[dX-(tan\theta)dY][/tex]

or what? I don't really understand what you wrote.

- #3

HallsofIvy

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sin(90- theta)= cos(theta) is one simplification.

- #4

ireland01

- 17

- 0

dalcde said:

[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

uart

Science Advisor

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

- #6

ireland01

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- 0

uart said:

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

yeah. that's it. thanks.

- #7

HallsofIvy

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And, by the way, it was the right side of the equation that was simplified, not the left side.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.

- #8

ireland01

- 17

- 0

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.

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.

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.

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

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.

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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