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Sin/cos/tan by hand?

by Goliatbagge
Tags: hand, sin or cos or tan
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Goliatbagge
#1
Feb5-14, 03:55 AM
P: 6
Does it exist a numerical method to calculate for example sin (42), sin (43), sin (44) etc by hand?
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adjacent
#2
Feb5-14, 05:06 AM
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P: 1,456
This may help.
jasonRF
#3
Feb5-14, 06:57 AM
P: 690
Quote Quote by Goliatbagge View Post
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 [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!


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