January 30th, 2017, 03:41 PM  #1 
Newbie Joined: Jan 2017 From: Norway Posts: 3 Thanks: 0  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 
January 30th, 2017, 04:45 PM  #2 
Newbie Joined: Jan 2017 From: Norway Posts: 3 Thanks: 0 
Solved it!

January 30th, 2017, 06:12 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,164 Thanks: 256 
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 06:20 PM. 
February 3rd, 2017, 04:24 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! 