When looking at the solution to a problem, the integral of (dy/y^2+1) turned out

Question

When looking at the solution to a problem, the integral of (dy/y^2+1) turned out to be arctan(y), where we substituted 1 for y, giving us C=tan^-1(1). When punching that into a calculator, you get a long decimal that ends up being equal to pi/4. I wouldn't have known it was pi/4 unless the solution told me, I would have just left it at the ugly decimal. Is the unit circle used in any way to come to that conclusion or is it just by chance that you should know that pi/4 is the simple form of .7853981634? If not the unit circle, what is used to know?

Explanation / Answer

well one should know that decimal is pi/4. or the best way is to set angle as degree while calculating inverse so that simply the calculator would display 45

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