Path: utzoo!attcan!uunet!samsung!zaphod.mps.ohio-state.edu!wuarchive!hp48sx From: hp48sx@wuarchive.wustl.edu (HP48SX Archive Maintainer) Newsgroups: comp.sys.handhelds Subject: Re: A strange feature (a bug?) Keywords: symbolic integration/differentation in DEG mode Message-ID: <1990Oct10.152505.2903@wuarchive.wustl.edu> Date: 10 Oct 90 15:25:05 GMT References: <1990Oct10.093506.8848@wuarchive.wustl.edu> <15930@shlump.nac.dec.com> Organization: Washington University in Saint Louis, MO Lines: 45 In article <15930@shlump.nac.dec.com> edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.)) writes: >In article <1990Oct10.093506.8848@wuarchive.wustl.edu>, >hp48sx@wuarchive.wustl.edu (HP48SX Archive Maintainer) writes: > >>If I try to evaluate dX(sin(X)) then I get: >>cos(x)*(dX(X)*(pi/180)) >>/* if the factor pi/180 should be applied, then it should be multiplied >> to the x in cox(x), but even this is not correct */ >>further EVAL gives: >>cos(X)*(pi/180) >> >>And we all know that cos(60) is 1/2 (the 60 is in degrees), and this is >>the correct result. But we still get the factor (pi/180) which will give >>me a wrong result. > >I think the result given is correct. If you plot sin(X) where X is measured in >degrees, the slope of that plot at X = 60 degrees will be pi/360. > >The derivative of sin(x) is cos(x) only if x is in radians. If the argument is >in degrees, then the derivative of sin(x) is cos(x)*(pi/180). > > > -- edp 60 degress = pi/3 radians. This is a FACT! thus sin( 60deg ) = sin( pi/3 RAD ) these two point are exactly at the same point on the curve, and thus the derivative must also be the same. I think that the error is because of the possibility of writing trigonometric functions in terms of the exponential function need the arguments of tr igonometric functions to be in radians. So if you are in degress mode, then the argument of a trigonometric function is considered to be a function (pi/180)* the argument. and if you take the derivative of a function on a function, then you get the outher functions derived times the inner derived. I am not sure if the results are correect for non real numbers. Like complex numbers. Povl -- ******************************************************* Povl H. Pedersen hp48sx@wuarchive.wustl.edu HP48sx archive maintainer