Hello, Thanks for reading this message.

To do with mathematics. Namely TrigONOmetry!

For a right angle triangle.  COS angle = Adjacent Side / Hypotenuse .

ie for a 3,4,5 Triangle...

cos (4/5) or cos(0.8) returns 0.69 in radians, And my book tells me to
first press the INV key, the inverse key,  then the COS key, followed by
0.8.  Which works fine on a calculator returning 36.9 degrees. But not so
in Turbo ver 3, as the INVerse function is un supported.

So, How can I write code to return degrees when supplied radians.
Moreover, are there sites containing mathematical functions to do just
this, which I may be allowed to use, and that will work OK in TP3.

In article <19971117013801.UAA28...@ladder02.news.aol.com>,

I'll solve half your question.

        ArcCos(x) = ArcTan(Sqrt(1 - Sqr(x)) / x);
        ArcSin(s) = ArcTan(x / Sqrt(1 - Sqr(x)));
        Tan(x) = Sin(x) / Cos(x);

ArcCos is the inverse of Cos etc.

As far as converting radians to degrees are concerned, just remember that
Pi = 180 degrees. Thus if x is a value in radians.
Then
        Degrees(x) = (180 * x) / Pi

In article <01bcf36d$31ba2980$02531...@lexlines.iafrica.com>,

Function arcsin(x:real):real; forward;

Function arcCos(x:real):real;
begin
  if abs(x)>0.001 then
     ArcCos:=ArcTan(Sqrt(1 - Sqr(x)) / x)
   else
     if x<0 then Arccos:=-pi/2+arcSin(-x)
            else Arccos:=pi/2-arcSin(x)
End;

Function ArcSin(x:real):real;
Begin
  if abs(abs(x)-1)>0.001 then
     ArcSin := ArcTan(x / Sqrt(1 - Sqr(x)))
  else
    if x<0 then ArcSin:=-pi/2+arcCos(-x)
           else ArcSin:=pi/2-arcCos(x)
End;

This is based on the fact that sin(x)=cos(pi/2-x). The threshold is drawn
from a hat.

A simple test for 0 or 1/-1 respectively might also work in most cases.
Note that handling these errors is important as they are caused in a
situation where the actual function is defined, unlike say the error
caused by tan() when cos(x)=0.

In article <64p8ju$...@kruuna.Helsinki.FI>, ronka...@cc.helsinki.fi (Osmo

Using the example I gave ie Cos(0.8) returning 0.69 radians...
0.69 * (180/pi) =  39.92 degrees

Unfortunately this differs from my text book example.

ie 0.8 inverse cos = 36.9 degrees a full 3 degrees difference!

On 17 Nov 1997 20:37:22 +0200, ronka...@cc.helsinki.fi (Osmo Ronkanen)
wrote:

{$N+}
type float=extended;

function arccos(c:float):float;
{        ArcusCosinus
  Input:    1 >=    c   >= -1
  Output:   0 <= arccos <= pi
          0 deg          180 deg

function arcsin(s:float):float;
{        ArcusSinus
   Input :  -1      <=   s    <=  1
   Output:  -pi/2   <= arcsin <= pi/2
           -90 deg              90 deg

function atan2(y,x:float):float;
{
  Oriented rotation angle from (1,0) to (x,y).
  May be interpreted as:
  Argument of the complex number x+i*y.
  x+iy = sqrt(sqr(x)+sqr(y))*exp(i*atan2(y,x))
  Angle phi of the representation of (x,y) in
  polar coordinates.
  r=sqrt(sqr(x)+sqr(y)) ; phi=atan2(y,x)
  x=r*cos(phi) ; y=r*sin(phi)  

  For compatibility with other programming
  languages, the order of parameters is (y,x)
  and the output range is

    -pi     < atan2 <=   pi
    -180 deg             180 deg

Hint: In order to compute the oriented rotation angle
from (x1,y1) to (x2,y2) for arbitrary non-null vectors
use the formula:

     phi = atan2(x1*y2-y1*x2,x1*x2+y1*y2) { *180/pi };

A more pedestrian and still safe implementation avoiding overflows
would be

function arcsin(s:float):float;
begin
  if s=-1 then arcsin:=-pi/2
  else if s=1 then arcsin:=pi/2
  else arcsin := arctan(s/sqrt(1-sqr(s)))
end;

function arccos(c:float):float;
begin
  if c=-1 then arccos:=pi
  else if c=1 then arccos:=0
  else arccos := pi/2 - arctan(c/sqrt(1-sqr(c)))
end;

or just

function arccos(c:float):float;
begin
  arccos := pi/2 - arcsin(c)
end;

If x compares FALSE to +-1 then abs(x)=1-delta and delta is not less
than the float-epsilon 'eps' for the chosen data type. With any
correct implementation of *, sqr(x) will be less than 1-eps and
1-sqr(x) greater than eps. As sqrt(eps) is greater than eps, the
denominator sqrt(1-sqr(x)) is greater than eps. As abs(x) is smaller
than 1 abs(quotient) is smaller than 1/eps. For every implementation
of floating point numbers 1/eps < MAXFLOAT. arctan(x) is never a
potential overflow problem because it is calculated via arctan(1/x)
and a transformation of the angle.

In article <19971118123400.HAA01...@ladder02.news.aol.com>,

Now what on earth do you want to achieve?

In article <01bcf36d$31ba2980$02531...@lexlines.iafrica.com>, "BASTARD"

That is..
  opp := 3;
  adj := 4;
  Hyp :=5;

  Angle := 180 * ArcTan(opp/adj)/pi { Returned 36.9 degrees! }

However...

  Angle := 180 * Cos(adj/hyp)/ Pi ; { Returned 39.?? degrees }

Why one works and the other not is beyond me.  I am grateful to all, for your
response and grateful that I found a solution. Which is to be used in the code
for the old Atari Classic, Missile Command.

Peace!

In article <19971121020900.VAA19...@ladder02.news.aol.com>,

Cos(36.9*pi/180) = 0.8 = adj/hyp

As I said before the result of cosine is not in radians. It is just a
number. Cosine takes an angle and produces the fraction between
adjacent side and hypotenuse.

If you want ArcCos you may try following:

function ArcSin(x:real):real;
begin
  if x=1.0 then ArcSin:=pi/2
    else if x=-1.0 then ArcSin:=Pi/2
      else ArcSin:=ArcTan(x/Sqrt(1.0-Sqr(x)));
End;

function ArcCos(x:real):real;
begin
  ArcCos:=pi/2-ArcSin(x)
end;

Try those and you will get 36.86990