Register to reply

Sin/cos/tan by hand?

by Goliatbagge
Tags: hand, sin or cos or tan
Share this thread:
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?
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
adjacent
#2
Feb5-14, 05:06 AM
PF Gold
adjacent's Avatar
P: 1,496
This may help.
jasonRF
#3
Feb5-14, 06:57 AM
P: 693
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!


Register to reply

Related Discussions
PF Photo Contest - Hand In Hand (6/29-7/5) Photography 2
Calculus, left hand, right hand limits. Calculus & Beyond Homework 3
Left hand trhread versus right hand thread General Engineering 4
Left hand and right hand circular polarization Classical Physics 2