My Math Forum Need some help with a proof

 Geometry Geometry Math Forum

January 30th, 2017, 02:41 PM   #1
Newbie

Joined: Jan 2017
From: Norway

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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 Newbie   Joined: Jan 2017 From: Norway Posts: 3 Thanks: 0 Solved it!
 January 30th, 2017, 05:12 PM #3 Senior Member   Joined: Aug 2012 Posts: 1,887 Thanks: 524 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.
 February 3rd, 2017, 03:24 PM #4 Newbie   Joined: Jan 2017 From: Norway Posts: 3 Thanks: 0 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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