
#1
Feb514, 03:55 AM

P: 6

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




#2
Feb514, 05:06 AM

PF Gold
P: 851

This may help.




#3
Feb514, 06:57 AM

P: 657

[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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