How can I use calculus to analyze errors in angle measurements?

In summary, the conversation is about finding the error in angles using calculus, specifically in the equation theta = Sin(o/h). The person is not familiar with calculus but needs help in finding the derivative of the sine function in order to solve the problem.
  • #1
lovemake1
149
1
URGENT URGENT ... Error Analysis in angle

Homework Statement



This is very urgent i could not find out how to find the error in my angles... using calculus
this is not my level but i must do it somehow..
i would love to see some steps that i can follow.

i know that for example E = mgh
dE/dm = gh
dE/dg = mh
dE/dh = mg


but how do do the same for
theta = Sin(o/h)

someone gave me this step but i do not know how to proceed from here...
d(theta)=1/sqrt(1-(o/h)^2)

please help... this is very urgent...

Homework Equations





The Attempt at a Solution

 
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  • #2


Relax. I'm going to sleep now, but I've posted a response in your Calculus thread. Check there.
 
  • #3


lovemake1 said:
i know that for example E = mgh
dE/dm = gh
dE/dg = mh
dE/dh = mg

Well, this is only true if these derivatives are partial derivatives (normally written as follows):

∂E/∂m = gh


lovemake1 said:
but how do do the same for
theta = Sin(o/h)

Well, you need to find out the derivative of the sine function, which is relatively simple. Do you know any calculus?
 
  • #4


no our grade 12 class is only past 1st term.
we have not yet learned calculus... but forsome reason we must know it by tom for our
assignment.. help
 

1. What is error analysis in angle?

Error analysis in angle is a method used to quantify and understand the sources and magnitude of errors in measuring angles. It involves identifying and measuring the uncertainties and variations in the measurement process, and determining how they affect the final angle measurement.

2. Why is error analysis important in measuring angles?

Error analysis is important because it allows us to determine the accuracy and reliability of angle measurements. It also helps identify any potential sources of error and allows us to make adjustments to improve the accuracy of our measurements.

3. What are the sources of error in angle measurements?

There are several sources of error in angle measurements, including human error, instrument error, environmental factors, and limitations of the measuring method. Human error can include misreading or incorrectly setting the measuring instrument, while environmental factors such as wind or vibrations can cause the instrument to fluctuate. The limitations of the measuring method, such as resolution or precision, can also contribute to errors.

4. How is error analysis performed in angle measurements?

Error analysis in angle measurements typically involves taking multiple measurements and calculating the average and standard deviation to determine the accuracy and precision of the measurements. It also involves identifying and quantifying any systematic errors and random errors, and determining their impact on the final angle measurement.

5. How can we reduce errors in angle measurements?

To reduce errors in angle measurements, it is important to follow proper measurement techniques and protocols, such as ensuring the instrument is properly calibrated and taking multiple measurements to reduce the impact of random errors. Using more precise instruments and reducing environmental factors, such as wind or vibrations, can also help improve the accuracy of angle measurements.

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