Re: trig functions
- To: mathgroup at yoda.physics.unc.edu
- Subject: Re: trig functions
- From: roland at afthp001.tuwien.ac.at (Roland Bauer)
- Date: Thu, 17 Jun 93 12:30:44 +0200
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Date: Mon, 7 Jun 93 21:30:10 -0500
From: bappadit at ecn.purdue.edu (Banerjee Bappaditya)
To: mathgroup at yoda.physics.unc.edu
Subject: trig functions
Hi!
I am trying to find the appropriate quadrant (from -Pi to Pi)
to which the inverses of trignometric functions evaluate. I have figured out the following rules...
if Sin[theta]>=0 && Cos[theta]>=0, angle = theta
if Sin[theta]>=0 && Cos[theta]<=0, angle = ArcCos[Cos[theta]]
if Sin[theta]<0 && Cos[theta]<0, angle = ArcSin[Sin[theta]] + Pi/2
if Sin[theta]=0 && Cos[theta]=-1, angle = -Pi
if Sin[theta]=-1 && Cos[theta]=0,angle = -Pi/2
if Sin[theta]<=0 && Cos[theta]>=0, angle = ArcSin[Sin[theta]]
How can I do this in Mma 1.2 so that a function
Angle[expression evaluating to a number] gives the correct theta ?
Or in other words, reduces the "expression " to modulo Pi.
I have (unsuccessfully!!!) tried
Angle[theta_] := If[Sin[theta]>=0 && Cos[theta]>=0,theta,
If[Sin[theta]>=0 && Cos[theta]<=0,ArcCos[Cos[theta]] ,
If[Sin[theta]=-1 && Cos[theta]=0,-Pi/2 ,
If[Sin[theta]<0 && Cos[theta]<0,ArcSin[Sin[theta]] + Pi/2 ,
If[Sin[theta]=0 && Cos[theta]=-1,-Pi ,
If[Sin[theta]<=0 && Cos[theta]>=0,ArcSin[Sin[theta]]
]]]]]]
Angle[theta_] := If[Sin[theta]>=0 && Cos[theta]>=0,theta,
If[Sin[theta]>=0 && Cos[theta]<=0,ArcCos[Cos[theta]] ,
If[Sin[theta]<0 && Cos[theta]<0,ArcSin[Sin[theta]] + Pi/2 ,
If[Sin[theta]<=0 && Cos[theta]>=0,ArcSin[Sin[theta]]
]]]]
It does not work in the 3rd Quadrant i.e. from -Pi/2 to -Pi.
I would appreciate any help.
thanks,
bappa.
Bappaditya Banerjee
bappadit at mn.ecn.purdue.edu
Ray W. Herrick Laboratories
Purdue University
West Lafayette, IN 47907
work : (317) 494 2132
(317) 494 2147
fax : (317) 494 0787
home : (317) 743 3982
Hi Bappa,
if you want to have a saw-tooth with the period a, You can define the
following function:
y[x_,a_]:=a(Mod[(x/a)+0.5,1]-0.5)
Then plot it with e.g.
Plot[y[x,360],{x,-500,+500}]
The function y transforms every angle into the range from
-(a/2) to +(a/2).
Maybe this was Your Problem?
Bye, Roland.
--
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