New guy and programming problem
09-01-2018, 12:23 PM
Post: #27
 Thomas Klemm Senior Member Posts: 1,804 Joined: Dec 2013
RE: New guy and programming problem
(08-28-2017 06:13 PM)Dieter Wrote:  On a 10-digit machine this already happens for 89,9995°...90,0005°.

We can use this difference-to-product formula to calculate e.g. $$1-\sin(89.9995°)=\sin(90°)-\sin(89.9995°)$$:

$$\sin \theta - \sin \varphi =2\sin \left({\frac {\theta - \varphi }{2}}\right)\cos \left({\frac {\theta + \varphi }{2}}\right)$$

And then since $$\theta = \frac{\pi}{2}$$ we can set $$\varepsilon = \frac {\theta - \varphi }{2}$$ and use $$\cos \left({\tfrac {\pi }{2}}-\varepsilon \right)=\sin \varepsilon$$ and end up with:

$$1 - \sin \varphi =2\sin^2 \varepsilon$$

Thus we set $$\theta=90$$ and $$\varphi=89.9995$$ and get:

90
ENTER
89.9995
-
2
÷
SIN

2
×

3.807717748e-11

(Calculated using an HP-41.)

Cheers
Thomas
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 Messages In This Thread New guy and programming problem - Skirmitch - 08-27-2017, 06:18 AM RE: New guy and programming problem - Dieter - 08-27-2017, 03:15 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 05:12 PM RE: New guy and programming problem - Dieter - 08-27-2017, 05:43 PM RE: New guy and programming problem - Paul Dale - 08-27-2017, 11:12 PM RE: New guy and programming problem - Dieter - 08-28-2017, 06:13 PM RE: New guy and programming problem - Paul Dale - 08-29-2017, 04:22 AM RE: New guy and programming problem - Garth Wilson - 08-27-2017, 09:14 PM RE: New guy and programming problem - Vtile - 09-01-2018, 07:28 PM RE: New guy and programming problem - John Keith - 08-27-2017, 05:52 PM RE: New guy and programming problem - Dieter - 08-27-2017, 06:28 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 06:03 PM RE: New guy and programming problem - Dieter - 08-27-2017, 06:11 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 06:23 PM RE: New guy and programming problem - pier4r - 08-27-2017, 07:52 PM RE: New guy and programming problem - Jlouis - 08-28-2017, 10:55 AM RE: New guy and programming problem - Skirmitch - 08-27-2017, 06:04 PM RE: New guy and programming problem - Skirmitch - 08-28-2017, 01:44 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 01:58 AM RE: New guy and programming problem - Skirmitch - 08-28-2017, 02:25 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 05:31 AM RE: New guy and programming problem - Skirmitch - 08-28-2017, 07:14 AM RE: New guy and programming problem - ndzied1 - 08-28-2017, 03:43 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 07:28 AM RE: New guy and programming problem - Logan - 08-28-2017, 02:20 PM RE: New guy and programming problem - Skirmitch - 08-28-2017, 06:11 PM RE: New guy and programming problem - Logan - 08-28-2017, 06:13 PM RE: New guy and programming problem - Thomas Klemm - 09-01-2018 12:23 PM RE: New guy and programming problem - Albert Chan - 09-01-2018, 02:16 PM RE: New guy and programming problem - Albert Chan - 09-02-2018, 06:14 PM RE: New guy and programming problem - Albert Chan - 09-02-2018, 09:21 PM RE: New guy and programming problem - sasa - 09-01-2018, 03:18 PM RE: New guy and programming problem - Albert Chan - 09-01-2018, 05:20 PM RE: New guy and programming problem - sasa - 09-01-2018, 05:33 PM RE: New guy and programming problem - Thomas Klemm - 09-01-2018, 04:28 PM RE: New guy and programming problem - Thomas Klemm - 09-02-2018, 07:33 PM RE: New guy and programming problem - Thomas Klemm - 09-02-2018, 09:33 PM RE: New guy and programming problem - Vtile - 09-02-2018, 09:40 PM RE: New guy and programming problem - Albert Chan - 09-03-2018, 10:32 PM

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