Calculate sides of polygon given side length and circumradius.

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Given $R$ and $a$ below, is it possible to calculate $n$ with just these values?

Example, say I have a circumradius of $10$, and a side length of $1$, is it possible to calculate $n$, rounded to the closest integer?

This is how far I've come (Wolfram Alpha's answer):

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But I would like to somehow eliminate $c_1$ and have no clue how. Using the above values, I tried to calculate $n$ using $R=1.3066$ and $a = 1$ which should result in $n=8$ but got nowhere close.

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