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Sin/cos/tan by hand?

  1. Feb 5, 2014 #1
    Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?
     
  2. jcsd
  3. Feb 5, 2014 #2

    adjacent

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  4. Feb 5, 2014 #3

    jasonRF

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    Of course you will turn these into radians ... but since all of your values are near [itex]\pi/4[/itex], I would use,
    [tex]
    \sin ( \pi/4 + x) = \sin(\pi/4) \cos(x) + \sin(x) \cos(\pi/4) = \left(\cos(x) + \sin(x) \right) / \sqrt{2}.
    [/tex]
    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.

    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!
     
    Last edited: Feb 5, 2014
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