How would you calculate the Tangent without a calculator?

Question

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.

Tables of the tangent function were made by Islamic mathematicians about a millenium ago. If my calculator dies, no problem, it is back to the tables. Any further multiplications needed to find a numerical answer can be done by slide rule. — André Nicolas, Jul 30 '13 at 19:53

score 2 · Accepted Answer · answered Jul 30 '13 at 19:55

2

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

answered Jul 30 '13 at 19:55

DJohnM

3,580

@DavisDude $\sin^2 (x)$ means $[\sin(x)]^2$. – Lord Soth Jul 30 '13 at 21:15

score 0 · Answer 2 · answered Jul 30 '13 at 19:51

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.

How would you calculate the Tangent without a calculator?

2 Answers2

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