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January 30th, 2017, 02:41 PM   #1
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Need some help with a proof

See attachment. I put a question mark behind the expression I need help deriving

Thank you for taking the time
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January 30th, 2017, 03:45 PM   #2
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Solved it!
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January 30th, 2017, 05:12 PM   #3
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We want the difference in the $y$-values, that's $\lvert \sin (\alpha + \beta) - \sin \alpha \rvert$. The absolute value is because in the general case the second point may be lower than the first one. I ignored the scaling factor and assumed radius $1$. I used $\alpha$ and $\beta$ for your $\varphi$ and $\mathrm d \varphi$.

Did you find a simplification beyond that?

Last edited by Maschke; January 30th, 2017 at 05:20 PM.
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February 3rd, 2017, 03:24 PM   #4
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Thank you for the reply.

My approach was to say that since d"phi" is infinitesimal (was this evident in the original post?), we can consider the arc as a line. The arc length will still be r*d"phi". And there we have it!
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