How to Calculate Uncertainty in Complex Equations with Trigonometric Functions

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To calculate the uncertainty in the theoretical value of R using the given equation involving trigonometric functions, one must apply the method of partial derivatives. Since basic uncertainty rules are insufficient for this complex equation, the discussion emphasizes the need to understand how to compute partial derivatives to assess the uncertainty accurately. The conversation also highlights the use of Excel for calculations, suggesting that learning to calculate derivatives can be done quickly. Participants express a need for guidance on applying these concepts effectively. Understanding partial derivatives is crucial for solving the uncertainty problem in this context.
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calculating uncertainty
I have a lab where I have to calculate the theoretical value of R using the following equation and then find the uncertainty in R.

R=(xCOS(y))*((-xSIN(y)-SQRT((xSIN(y))^2-2*-9.8*z))/-9.8)
*I know the values of x,y,z and their respective uncertainties.

The problem is that we have only learned basic uncertainty rules (i.e. for multiplication/division you add the %uncertainty, for addition/subtraction you add the absolute uncertainties). This is much more complicated since I have to deal with SIN/COS and square roots. I was searching around and it seems that I have to calculate the partial derivative or differentials. I am not familiar with differentials and I have no idea how to solve this problem. If anyone can offer any help whatsoever it would be greatly appreciated or anywhere where I can find this information.

i'm using excel if that makes any difference.
 
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Do you know how to calculate a derivative? If so, it shouldn't take more than a minute to learn how to take a partial derivative.
 
take extremes!
simple and perfect
 
i know how do to partial derivatives but is the uncertainty just the partial derivative of the equation.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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