Sine Multiplication

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Discussion Overview

The discussion revolves around the manipulation of sine functions in mathematical equations, particularly in the context of continuous uniform distributions and beta distributions. Participants explore the implications of variable values in equations and the correct application of mathematical functions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether to multiply all numbers in the equation before applying the sine function or to apply the sine function first to the number next to it.
  • Another participant seeks clarification on the expression being discussed, suggesting it may relate to Laplace transforms and providing a potential form of the function.
  • A participant expresses confusion about the original poster's terminology and requests clearer examples to understand the question better.
  • One participant mentions that they have resolved their issue regarding the sine equation but notes that different cases may yield different results.
  • Another participant corrects a claim about carbon-8's decay process, stating it does not decay by alpha emission.
  • A later reply encourages the use of LaTeX for mathematical expressions to improve clarity in future discussions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the sine function or the implications of variable values in the equations. There are competing views on the decay process of carbon-8, and the discussion remains unresolved regarding the best practices for mathematical expression clarity.

Contextual Notes

Participants express uncertainty about the definitions and conditions of the equations discussed, particularly regarding the variable t and its implications in different contexts. There are also unresolved mathematical steps related to the manipulation of the sine function.

Vilhjalmur Haldorson
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TL;DR
Sine Multiplication
Hi, I am doing a sine quation which has multiple numbers along the line.I was wondering when multiplying the equation out do I multiply all the numbers then sin function that number or do I sin the number beside the sine function and then multiply it out?
The equation is: sin h bt/ bt.
I also have another question, if t does not equal 1 and an equation requires that it equals one then can I use 0.66 instead of one or is the equation set for when t=1 and cannot be used with t=0.66?
 
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Lets start at the beginning:

Is this something that has to do with using Laplace transforms?

$$f(t)=\sinh(bt)=\frac{e^{bt}-e^{-bt}}{2}$$

or is your expression $$\frac{\sinh(bt)}{bt}$$ or $$\frac{\sin(hbt)}{bt}$$ ?
 
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Vilhjalmur Haldorson said:
Hi, I am doing a sine quation which has multiple numbers along the line.I was wondering when multiplying the equation out do I multiply all the numbers then sin function that number or do I sin the number beside the sine function and then multiply it out?
What does "multiple numbers along the line" mean? Also, your question would be more comprehensible if you provided an example of what you're talking about.
Vilhjalmur Haldorson said:
The equation is: sin h bt/ bt.
First, this is not an equation -- an equation expresses the equality of two expressions (or possibly more) and has an = symbol between the expressions.
Second, what you have written is too ambiguous for us to even tell what it's supposed to represent.
Vilhjalmur Haldorson said:
I also have another question, if t does not equal 1 and an equation requires that it equals one then can I use 0.66 instead of one or is the equation set for when t=1 and cannot be used with t=0.66?
What equation? Why does some "equation" require that t = 1?

You're going to have to be a lot clearer in your questions if you want reasonable replies.
 
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Sorry Im doing a continuous uniform distribution from the beta distribution using Mx= sinh(bt)/bt but Ive already fugured it out.It doesnt matter they both come out the same way.But that is not always the case. , and t=1 in a hypoerbola , but t=0.66 for me . Im doing the alpha decay of the carbon 8 to Nitrogen and C13. but eh stable alpha soes not seem to equate out.SO I am doing the uniform distribution from the beta distribution and then the continuance of the beta distribition at (x-a)^a-1(b-x)^B-1 / B(a,B) transpose (b-a)^a+B+t , a< x< b, a>0,,B > 0 and then normally distribute it, but Ive been thinking mybe I should do a student t instead first.
 
Vilhjalmur Haldorson said:
Im doing the alpha decay of the carbon 8 to Nitrogen and C13.
Carbon-8 does not decay by ##\alpha##-emission. It decays by double proton emission to beryllium-6.
 
That's great that you figured it out.

In the future, please learn to use latex to enter your math expressions. We have a simple guide. See my signature below for the link to Mathjax/latex help.
 
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