Uncertainty for n using calculus

In summary, the conversation is discussing the calculation of uncertainty for the variable n, which is defined as Sin((Dm + a)/2) over Sin(a/2). The speaker is unsure how to handle the sin functions and mentions being new to this type of calculation. They have already calculated the uncertainty and values for Dm and a. The other person provides a hint involving the partial derivative of a function with multiple independent variables.
  • #1
Homework Statement
Hi, I need help ASAP with finding the uncertainty of n i've been trying for an hour to figure out how to tackle this question can I please have some guidance as to how to approach the question?!! Thanks in advance.
Relevant Equations
n=(Sin((Dm + a)/2))/(Sin(a/2))
i'm thinking of differentiating the inside of both sin functions but I'm not sure what to do with the sin. if anything, I'm new to this sort of uncertainty calculation. I have calculated the uncertainty and values for both Dm and a in advance.
 
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  • #2
I believe you first have to compute ##\frac{dn}{da}## and ##\frac{dn}{d(Dm)}## via a little quotient + chain rule. Then you can take the sum of all of the ##dn##'s.
 
  • #3
SHAWN JAMES said:
Homework Statement:: Hi, I need help ASAP with finding the uncertainty of n I've been trying for an hour to figure out how to tackle this question can I please have some guidance as to how to approach the question?! Thanks in advance.
Relevant Equations:: n=(Sin((Dm + a)/2))/(Sin(a/2))

i'm thinking of differentiating the inside of both sin functions but I'm not sure what to do with the sin. if anything, I'm new to this sort of uncertainty calculation. I have calculated the uncertainty and values for both Dm and a in advance.

Hint: $$ df = \frac {\partial f } { \partial x} dx + \frac {\partial f } {\partial y} dy ~+ ... ~$$
where f = f(x,y, ...) and x, y ... are assumed to be independent variables.
 
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1. What is uncertainty for n using calculus?

Uncertainty for n using calculus refers to the amount of variation or error in a mathematical equation or formula that includes the variable n. It is a measure of how much the value of n can change and affect the overall outcome of the equation.

2. How is uncertainty for n calculated using calculus?

Uncertainty for n is typically calculated using the principles of calculus, specifically the concept of differentiation. This involves finding the derivative of the equation with respect to the variable n, and then using this derivative to determine the potential range of values for n.

3. Why is uncertainty for n important in scientific research?

Uncertainty for n is important in scientific research because it allows for a more accurate understanding of the results and conclusions drawn from an experiment or study. It helps to account for any potential errors or variations in the data and allows for more precise and reliable findings.

4. How does the value of n affect uncertainty for n using calculus?

The value of n directly affects the uncertainty for n using calculus, as a larger or more extreme value of n will typically result in a larger uncertainty. This is because a higher value of n will have a greater impact on the overall outcome of the equation.

5. What are some potential sources of uncertainty for n in scientific experiments?

There are several potential sources of uncertainty for n in scientific experiments, including measurement errors, equipment limitations, and variations in environmental conditions. Human error and sample size can also contribute to uncertainty for n in some cases.

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