Calculate Sin/Cos/Tan By Hand - No Calculator Needed!

[Goliatbagge]

Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?

 

[adjacent]

This may help.

 

[jasonRF]

Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?

Of course you will turn these into radians ... but since all of your values are near \pi/4, I would use,
<br /> \sin ( \pi/4 + x) = \sin(\pi/4) \cos(x) + \sin(x) \cos(\pi/4) = \left(\cos(x) + \sin(x) \right) / \sqrt{2}.<br />
Your values of x are -\pi/180, -2 \pi/180, - 3 \pi/180, ... which are small, so you can take the first few terms in the Taylor series for sin and cos near zero. Even approximating \cos(x) \approx 1 and \sin(x)\approx x should get you several correct digits for the exact examples you gave.

jason

EDIT: I now see that this was included in adjacent's link above. I had just read the first part with the Taylor series about zero ... Oops!