Estimate relative error using differentials

In summary, to estimate the relative errors of the area of a right triangle with hypotenuse H using differentials, you need to find the differential of the area A, which is equal to (1/4)H^2sin(2theta). This can be done by finding the derivative, which should be provided in your textbook. Additionally, a minute of arc, 1', is equivalent to 1/60 of a degree.
  • #1
DevoMci
1
0
Area of right triangle with hypotenuse H is

A=(1/4)H^2sin(2theta)

where theta is one of the acute angles.

Use differentials to estimate the relative errors of the area A if H=4cm and theta is measured to be 30 degrees with an error of measurement of 15 minutes of arc.

note: a minute of arc, 1' is approximately equal to (1/60) of a degree.

I'm not quite sure what a measurement of arc is and whether I'm supposed to find the derivative or what? I am so lost, thanks in advance.
 
Physics news on Phys.org
  • #2
DevoMci said:
Area of right triangle with hypotenuse H is

A=(1/4)H^2sin(2theta)

where theta is one of the acute angles.

Use differentials to estimate the relative errors of the area A if H=4cm and theta is measured to be 30 degrees with an error of measurement of 15 minutes of arc.

note: a minute of arc, 1' is approximately equal to (1/60) of a degree.

I'm not quite sure what a measurement of arc is and whether I'm supposed to find the derivative or what? I am so lost, thanks in advance.
You need to find the differential of A, dA. Your book should have some examples of how to find the differential.

Also, unless I'm missing something, one minute of arc, 1', is exactly equal to 1/60 of a degree.
 

Related to Estimate relative error using differentials

1. How do you define relative error?

Relative error is a measurement of the difference between the estimated value and the actual value of a quantity, expressed as a percentage of the actual value. It is used to assess the accuracy of a measurement or calculation.

2. What is the formula for calculating relative error using differentials?

The formula for calculating relative error using differentials is: Relative Error = (Change in estimated value / Actual value) * 100%. This formula takes into account the change in the estimated value and the actual value, expressed as a percentage.

3. How do you interpret relative error using differentials?

Interpreting relative error using differentials involves comparing the estimated value to the actual value and determining the difference as a percentage. A higher relative error value indicates a larger difference between the estimated and actual values, while a lower relative error value indicates a smaller difference.

4. What are the advantages of using differentials to estimate relative error?

Differentials allow for a more accurate estimation of relative error by taking into account the change in the estimated value. This can be especially useful when dealing with complex calculations or measurements with small margins of error.

5. How is relative error using differentials used in scientific research?

Relative error using differentials is commonly used in scientific research to assess the accuracy and precision of measurements and calculations. It is also used to compare different methods or instruments for measuring a quantity, and to determine the level of uncertainty in experimental results.

Similar threads

Estimating maximum percentage error using partial differentiation
    • Calculus and Beyond Homework Help
Replies
10
Views
2K
Relative Error of Right Triangle Area
    • Calculus and Beyond Homework Help
Replies
3
Views
5K
What Is the Optimal Angle Theta to Minimize Journey Time in Calculus?
    • Calculus and Beyond Homework Help
Replies
28
Views
1K
Finding Area of Shaded Segment in Circle Using Calculus
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Using differentials to estimate the maximum possible error
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Error estimation using differentials
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
MHB Using differentials to estimate error
    • Calculus
Replies
2
Views
4K
Problem with Approximations Using Differentials
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
I On error estimates of approximate solutions
    • Differential Equations
Replies
1
Views
723
Using Partial Derivatives to estimate error
    • Calculus and Beyond Homework Help
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top