- #1
bigevil
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Homework Statement
For my lab work, I have created a theoretical model that goes something like:
[tex]
T = \sqrt{\frac{ks^2}{x \sin \theta \cos^2\theta}}
[/tex]
where k is a constant, and the variables to be differentiated are x, theta and s. How do I find the error of T? I can find the errors of x and s (dx/x and ds/s) from experiment. And of course
[tex]d\theta / \theta[/tex] can also be found from the instrument.
The Attempt at a Solution
Differentiating the term for theta,
[tex]\frac{dF}{d\theta} = -\frac{1}{2} \sqrt{\frac{1}{\sin\theta \cos^2 \theta}} \cos\theta (1 - 3\sin^2\theta)[/tex]
It's easier to differentiate the other two. Anyway, I have:
[tex]\frac{dT}{T} = \frac{ds}{s} + \frac{1}{2}\frac{dx}{x} + \frac{(3\sin^2\theta - 1)\cos\theta}{2}d\theta[/tex]
How can I express the last term in a [tex]d\theta / \theta[/tex] form? The only thing I can think of at the moment is using a small angle approximation, but I don't know how to justify that. And also, clearly, if I could use that, the small angle approximation for cosine has a square term.