# Talk:Arcsin as an Integral

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This entry has two purposes: 1) to show geometric sine and analytic (i.e. defined as power series) are the same. 2) to remove circularity in reasoning about derivative of sine function, limit of sin(x)/x, and area proofs.

Limit of Sine of X over X/Geometric Proof uses Area of Sector. Area of Sector assumes the area of sector is proportional to the length of the arc. This is true. And it looks plausible on a blackboard, but it is a hand wave. The only way to prove is to do the integrals. But this would require you to do a u-substitution involving $sin$. But you can't do this because limit of sin(x)/x is used to prove the Derivative of Sine Function. I am trying to break this circularity. --Pelliott (talk) 05:19, 29 January 2019 (EST)

Fair enough. We can tidy up later. --prime mover (talk) 05:33, 29 January 2019 (EST)

As it is now, the proofs of the lemmas do not show on the main page. Is this correct? Do we need to change the onlyinclude s ? --Pelliott (talk) 17:40, 29 January 2019 (EST)

I am hazy on how onlyincludes work please help --Pelliott (talk) 17:45, 29 January 2019 (EST)

House style is that the statement only of the lemma / theorem / corollary etc. is transcluded into its parent page. It makes the proof easier to follow, and makes the page shorter, as the steps come in easily-conprehended blocks. If you have a great wall of text it makes it more difficult to follow. --prime mover (talk) 18:08, 29 January 2019 (EST)