Flags for trig representation (positive frequency*t+phase)?

[wsprague]

Hi all,

In a calculation (working through a Laplace Transform problem in a circuits book), I get a result "cos ((3/4)*pi - 2*x)", but I would much prefer something with a positive value for the variable and the phase constant, preferably with the phase to the right instead of the left, like "cos(2*x + BLAH)".

Is there a flag or a trig symbolic rewrite to make this happen?

I tried using "trigcos()" on it but it doesn't change it.

I am using the 2018-07-xx firmware.

(Also "trigcos(cos(-x+pi/2))", just playing around, yields "sin(x)" which seems like the wrong rewrite for the command. Just saying.)

Thanks for the help!

[parisse]

There is no way for the CAS to guess that cos(2x-3/4*pi) is better than cos(3/4*pi-2x). If you want to negate all cos arguments in an expression, you can run subst(expression,cos,x->cos(-x)).
cos(-x+pi/2) is auto-simplified to sin(x), then trigcos will not do anything, because trigcos applies the relation sin(x)^2+cos(x)^2=1 and nothing else (if you run trigcos(cos(-x+pi/2)^2), you will get 1-cos(x)^2).

[wsprague]

(08-19-2018 02:18 PM)parisse Wrote:  There is no way for the CAS to guess that cos(2x-3/4*pi) is better than cos(3/4*pi-2x). If you want to negate all cos arguments in an expression, you can run subst(expression,cos,x->cos(-x)).
cos(-x+pi/2) is auto-simplified to sin(x), then trigcos will not do anything, because trigcos applies the relation sin(x)^2+cos(x)^2=1 and nothing else (if you run trigcos(cos(-x+pi/2)^2), you will get 1-cos(x)^2).

Pr Parisse -- that is a big help, thank you.

I will keep working on getting *all* sin and cos results to be represented as an equivalent "cos(gamma*t + phi)", but I think that is in the homework stage for me, getting to know the subst() transformation better.