Sin/cos/tan by hand?

  1. Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?
  2. jcsd
  3. adjacent

    adjacent 1,540
    Gold Member

    This may help.
  4. jasonRF

    jasonRF 855
    Science Advisor
    Gold Member

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


    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!
    Last edited: Feb 5, 2014
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