Differentiate Trig Homework: Find Uncertainty in Measured Angle

AI Thread Summary
The discussion focuses on finding the uncertainty in a measured angle derived from a triangle formed by a cardboard and a stack of books. The angle is calculated using the inverse sine function, with the hypotenuse measured at 33 cm and the height variable. The uncertainties in both the hypotenuse and height are noted as ±0.005 m. The user seeks guidance on how to differentiate the angle concerning these measurements and how to apply the error propagation formula. The conversation emphasizes the need for clarity in differentiating the angle with respect to the measured dimensions to accurately assess uncertainty.
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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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If x = a/b, then the maximum error in measurement is
Δx/x = Δa/a + Δb/b
 
d(theta)=1/sqrt(1-(o/h)^2)

now how should i ?

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

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