Differentiate Trig Homework: Find Uncertainty in Measured Angle

In summary, the conversation discusses a student's project where they must find the uncertainty in the angle measured for a cardboard triangle. The student is seeking guidance on how to differentiate between the uncertainty in the opposite and hypotenuse measurements. A formula is suggested, but the student is unsure of how to use it.
  • #1
lovemake1
149
1

Homework Statement



we have been doing some error analysis in school, but they were very straight forward for example. Centripetal Acceleration : Fc = 4pi^2 m R / T^2


however, for my project i must find the uncertainty in the angle that i measured.
the angle is formed by a cardboard sitting on pile of books creating a triangle.
Hypothenus = 33cm
Height = Variable ( Changes according to the stack of the book)

please help ! differentiate theta = inverseSin(Opposite/Hypothenus)




Homework Equations



theta = inverseSin(Opposite/Hypothenus)

The Attempt at a Solution



well since i measurd these distances with a ruler

the uncertainty for hypothenus would be +- 0.005m (last half digit of a number)
and the uncertainty for heght is the same + - 0.005m (last half dight of a number)

how do i use these to differentiate for one another?
which formurla woudl i use pleaes help !
 
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  • #2
If x = a/b, then the maximum error in measurement is
Δx/x = Δa/a + Δb/b
 
  • #3
d(theta)=1/sqrt(1-(o/h)^2)

now how should i ?

HELP please just differentiate for opposite and hypothenus for me please...
 
  • #4
d(theta)=1/sqrt(1-(o/h)^2)
From where did you get this expression?
What it represents?
 

1. How do I differentiate trig homework?

To differentiate trig homework, you will need to use the chain rule and the product rule. First, identify the trigonometric functions involved in the problem. Then, use the chain rule to find the derivative of the outer function and the product rule to find the derivative of the inner function. Finally, combine the two derivatives to find the overall derivative of the trigonometric function.

2. What is the importance of finding uncertainty in measured angle?

Finding uncertainty in measured angle is important because it helps us understand the accuracy and precision of our measurements. It allows us to account for any errors or variations in our measurements and provides a range of possible values for the angle. This is especially crucial in scientific experiments and calculations where the exact value of an angle can greatly impact the results.

3. How do I find uncertainty in measured angle?

To find uncertainty in measured angle, you will need to use the error propagation formula. This formula takes into account the uncertainties in the measured values and calculates the overall uncertainty in the final result. You will also need to determine the sensitivity of the measuring device used to measure the angle, as this will affect the level of uncertainty.

4. Can uncertainty in measured angle be negative?

No, uncertainty in measured angle cannot be negative. It represents the range of possible values for the angle, and a negative uncertainty would not make sense in this context. If your calculation results in a negative uncertainty, double-check your calculations and make sure you are using the correct units.

5. How can I reduce uncertainty in measured angle?

To reduce uncertainty in measured angle, you can use more precise measuring devices, take multiple measurements and calculate the average, and minimize any external factors that could affect the measurement (such as wind or vibrations). It is also important to use proper measurement techniques and record all measurements accurately.

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