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I was just curious as to how you would calculate it without a calculator. I don't care if it's in radians or degrees, but I just would like it to be specified.

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2 Answers

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Use Taylor series for sin in radians:$$\sin(x) = x-\frac{x^3}{3!}+\frac{x^5}{5!}-...$$ Then calculate tan:$$\tan(x)=\frac{\sin(x)}{ \sqrt{1-\sin^2(x)}}$$

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The Taylor series for $\sin$ and $\cos$ converge quickly enough that a few digits of accuracy is possible with relatively few computations by hand (generally, computing 2-3 terms will give about two digits of accuracy). Then the division can be carried out.

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