New guy and programming problem

09012018, 12:23 PM
Post: #27




RE: New guy and programming problem
(08282017 06:13 PM)Dieter Wrote: On a 10digit machine this already happens for 89,9995°...90,0005°. We can use this differencetoproduct 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 x² 2 × 3.807717748e11 (Calculated using an HP41.) Cheers Thomas 

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