HP Forum Archive 14

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CAS vs Plot Message #1 Posted by Mike (Stgt) on 16 Nov 2004, 8:26 a.m. Hi all! I am _not_ the mathematician so I need some help for following function I found in the CAS examples. SIN(X)^2 ------------ COS(X)TAN(X) ---------------------- = 1 _ +------------------ |/ SIN(X)COS(X)TAN(X) On the emulated HP40 with CAS version 4 (4/27/2000) I get this result too (after TAN2SC and EXPAND). But if I plot this function it shows a square wave between 1 and -1. Question: CAS does not respect the sign? Ciao.....Mike

Re: CAS vs Plot Message #2 Posted by Dave Shaffer on 16 Nov 2004, 9:22 a.m., in response to message #1 by Mike (Stgt) Mike, It depends on where the square should be on the top term. Is it (sin(x))^2 (i.e. the entire sin function that is squared) or sin (x^2) (i.e. the argument of the sin function that is squared)? If it is the first, then this set of trig functions does not even have to be evaluated! It reduces exactly to 1. Why? Well, you can express tan(x) as sin(x)/cos(x). If you do this, then everything cancels out. In the denominator square root, for instance, you'd get (leaving off the (x) arguments for ease of notation) sqrt( sin cos (sin/cos) ) = sqrt (sin^2 ) = sin Similarly, the top of your equation reduces first to sin^2/sin = sin Leaving for the final step, sin/sin = 1

Re: CAS vs Plot Message #3 Posted by Mike (Stgt) on 16 Nov 2004, 11:03 a.m., in response to message #2 by Dave Shaffer Thank you Dave for your investigation, but I am not convinced: in the denominator you may reduce to sqrt(sin^2) what is never negative due to square. Further reduction would be abs(sin). But as numerator you get after reduction sin^2/sin what keeps the sign of sin (even if you keep your fingers crossed <G>). So the overall reduction would be sin/abs(sin) what is 1 or -1 every now and again. So the plot on the HP-40G revealed a nasty surprise (as ugly as sin or remissible peccadillo?) in it's own CAS. Bombs on Babylon! Mathematical gomorrah!! The 40G was made to use at school. Ciao.....Mike (sinning, pondering, scapegoat) No-no abs(sin) has nothing to do with absinth and I did not drink too much of it... Edited: 16 Nov 2004, 11:05 a.m.

Re: CAS vs Plot Message #4 Posted by Mark A. Ordal on 18 Nov 2004, 9:18 a.m., in response to message #3 by Mike (Stgt) Mike says: "Thank you Dave for your investigation, but I am not convinced: in the denominator you may reduce to sqrt(sin^2) what is never negative due to square." NO! because sqrt(anything^2) = +/-anything So, in the end, Mike's original expression reduces to *either* +1 or -1, depending on your choice of root. The "abs" function has no relevence here. (I am assuming that when Mike writes "SIN(X)^2" he means exactly that---namely "(SIN(X))^2" which mathematicians prefer to write as "SIN^2(X)".) --Mark

Re: CAS vs Plot Message #5 Posted by Mike (Stgt) on 22 Nov 2004, 3:54 a.m., in response to message #4 by Mark A. Ordal Yep - you are correct! Now when I read sqrt(anything^2) = +/-anything I remember. How could I forget. So the correct answer would be sign(sin(x)) or abs(sin(x))/sin(x)? Ciao.....Mike

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