       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

```    Received: from reggae.concert.net by afthp001.tuwien.ac.at with SMTP
(16.6/16.2) id AA08683; Wed, 9 Jun 93 17:02:04 +0200
Received: from yoda.physics.unc.edu by reggae.concert.net (5.59/tas-reggae/8-15-92)
id AA29347; Wed, 9 Jun 93 02:59:52 -0400
id AA05299; Wed, 9 Jun 93 00:31:00 EDT
id AA05295; Wed, 9 Jun 93 00:30:59 EDT
Message-Id: <9306090430.AA05295 at yoda.physics.unc.edu>
Date: Mon, 7 Jun 93 21:30:10 -0500
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.

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).

Bye, Roland.

--

---------------------------------------------------------------------------
| Roland BAUER                         tel: +43 (222) 58-801 / 4861       |
| Abt. Foerdertechnik                  fax: +43 (222) 586-58-47           |
|                                      email: bauer at afthp001.tuwien.ac.at |
| Getreidemarkt 9                                                         |
| A - 1060 VIENNA / AUSTRIA / EUROPE                                      |
---------------------------------------------------------------------------
| Technische Universitaet Wien                                            |
| Institut fuer Allgemeine Maschinenlehre und Foerdertechnik              |
| Abteilung Foerdertechnik (321/2)                                        |
---------------------------------------------------------------------------

```

• Prev by Date: re:red-green stereograms
• Next by Date: Re: 2D Integration
• Previous by thread: Re: trig functions
• Next by thread: Problem with Times. Bug ????