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Power series for the inverse cosine
The inverse cosine has the power series development
Explanation
The first derivative of the inverse cosine is
We now determine the further derivatives
At point x = 0 you get
We're going to fill out the Taylor series
Now we see a regularity, because
so that
Example 1
You can see that cos-1(0) = 1,57079632…, because
General form
You can write the power series as a sum