Monday, 23 July 2018

trigonometry - Where is this trig equation derived from?




In the first, top rated, comment on the original post linked below, the author wrote the function r=cos(x)1cos(x). I do not understand how they got to this equation. I get how they solved for x in their first step. Can you please explain how they solved for r.



This is the picture of the problem, where we are solving for r, given x=n22n



enter image description here



Original Post
Numbers of circles around a circle


Answer



In the right Triangle, we can write cosx as

Base divided by the hypotenuse



cosx=rr+1



1cosx=1+1r



1r=1cosx1
1r=1cosxcosx
r=cosx1cosx


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