"Timothy R. Cook" <tim### [at] scifi-fantasycom> wrote in message
news:3CAA1645.34E2D335@scifi-fantasy.com...
> 25ct wrote:
> > You mean "SOHCAHTOA"?  I learnt that at school. I used to be good
> > at trig. with a tables book... (still got it),  wish I kept it up...
>
> I still find it easier to picture, at least, using vectorised versions.
> e.g.
> x = r*COS(t)
> y = r*SIN(t)
> t = TAN-1(x/y)
> r = SQRT((x^2)+(y^2))

     Tim, sorry, I'm now lost with this... I recognise it though. I think our teacher
showed us the same?

    I could do with someone taking me through the basics again... Are you game? I'd
appreciate it.

   If it's ok, mail me or take me through it here, either way, no probs. I used to
enjoy doing trig. when I was younger.

     ~Steve~


>
> --
> Tim Cook
> http://empyrean.scifi-fantasy.com
>
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> D++(---) G(++) e*>++ h+ !r--- !y--
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25ct wrote:
> "Timothy R. Cook" <tim### [at] scifi-fantasycom> wrote:
> > I still find it easier to picture, at least, using vectorised'
> > versions.
> > e.g.
> > x = r*COS(t)
> > y = r*SIN(t)
> > t = TAN-1(x/y)
> > r = SQRT((x^2)+(y^2))
> 
> Tim, sorry, I'm now lost with this... I recognise it though. I think
> our teacher showed us the same?
> I could do with someone taking me through the basics again... Are
> you game? I'd appreciate it.

No problemmo.  I actually found vectors to be enjoyable.  Probably
the only part of math in high school I ever did like.  (Actually, I
originally was taught vectors in Physics, but...)

(Side note:  I use the right-hand rule, so Y is north, X is east)

+Y
|   . endpoint (distance r from origin)
|  /
| /., angle (theta)
|/   `,
+-------- +X

If you think about the vector in terms of x & y, you realise that
it's the hypoteneuse of a right triangle whose base and perpendicular
side are the axes.  So.  You get a right triangle:
      
       .
      /|
     / |
 r  /  | y
   /   |
  /   _|
 /?  | |
o------+
   x

Something about r: it's a radius of a circle with centre at o.
(Which is why I use 'r'.  The only reason I point this our is
'cuz when you rotate an object around a point, the other end
is going in a circle, and the angle is how far it's turned.)

Anyways.  If you know the angle and radius (as with velocity
vectors), the length of x is equal to the radius times the
cosine of the angle.  The length of y is equal to the radius
times the sine of the angle.  If you know x and y and want
to find the radius, use the Pythagorean theorem: a^2 + b^2 = c^2
(or, radius equals square root of x squared plus y squared).
The angle is the arctangent of x divided by y.

Vector addition simply strings together several vectors and
figures out the vector between start/end points.

This is helpful for making a CSG of a box of arbitrary size.
If I have a box at 0,0,0 and it has a scale of 1,2,0.5 and
I want to cut it in half diagonally along the xz surface,
how big do I need to make the differencing box, and how much
does it need to be rotated?  I know X and Y.  So.  It needs
to be SQRT((1^2)+(0.5^2)) along its x axis, or 1.11803399.
It needs to be rotated TAN-1(1/0.5), or 63.4349488 degrees.

-- 
Tim Cook
http://empyrean.scifi-fantasy.com

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N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
D++(---) G(++) e*>++ h+ !r--- !y--
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I was taught a simple rhyme a very long time ago and it stuck.

Silly Old Harry (S=O/H)
Caught A Herring (C=A/H)
Trawling Off America (T=O/H)

Daft, but it works for me.

Dave

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"Timothy R. Cook" <tim### [at] scifi-fantasycom> wrote in message
news:3CAA384B.F4BF1CB8@scifi-fantasy.com...

<cut and pasted into notepad>

  Thanks 'very' much Tim, I'm working through this.

     BR,

    ~Steve~




> Tim Cook
> http://empyrean.scifi-fantasy.com
>
> -----BEGIN GEEK CODE BLOCK-----
> Version: 3.12
> GFA dpu- s: a?-- C++(++++) U P? L E--- W++(+++)>$
> N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
> PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
> D++(---) G(++) e*>++ h+ !r--- !y--
> ------END GEEK CODE BLOCK------

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Except that Trawling off American would be (T-O/A)

:)

Grim

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Hi Dave Brickell, you recently wrote in povray.binaries.images:

> I was taught a simple rhyme a very long time ago and it stuck.
The rhyme I was taught only listed the ratios since we could rememeber
the order sin, cos, tan. It went like this:

Old Henry
And His 
Old Aunt

I still use it everytime I need to figure an angle out :-)

- Lutz
  email : lut### [at] stmuccom
  Web   : http://www.stmuc.com/moray

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Yeah I spotted my error as soon as I posted it yet I did not spot it when I
read it through twice before posting it. I am sure this is some kind of
phenomenon as it has happed to me before.

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On Wed, 3 Apr 2002 00:22:47 -0800, Dave Brickell wrote...
> I was taught a simple rhyme a very long time ago and it stuck.
> 
> Silly Old Harry (S=O/H)
> Caught A Herring (C=A/H)
> Trawling Off America (T=O/H)
> 
> Daft, but it works for me.

The Cat Sat
On An Oven
And Howled Horribly

TCS     Tan = Opposite/Adjacent
OAO  =  Cos = Adjacent/Hypotenuse
AHH     Sin = Opposite/Hypotenuse

Is how I remember it.

Jamie.

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