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trigonometry
MUFF WIGGLER Forum Index -> Music Tech DIY  
Author trigonometry
AnalogFan
Hi there,

i need some help with "trigonometry"



i need find the metric coordinates of pin 1.
we know the angle and the hypotenuse, what to do next?

thnx in advance.
diode_destroyer
So with respect to the middle axes/coordinate system, pin 1 is to the right by 6.5sin(45deg) (calculator in deg mode!) = 6.5/sqrt(2) = 4.59619 and it is down by 6.5cos(45) = (also) 6.5/sqrt(2) = 4.59619. (In whatever units your original numbers are in, e.g. mm.)
AnalogFan
diode_destroyer wrote:
So with respect to the middle axes/coordinate system, pin 1 is to the right by 6.5sin(45deg) (calculator in deg mode!) = 6.5/sqrt(2) = 4.59619 and it is down by 6.5cos(45) = (also) 6.5/sqrt(2) = 4.59619. (In whatever units your original numbers are in, e.g. mm.)


indeed, thanx very much. awesome

i did research and your info is the same, but i stumbled on the squareroot.
ranix
here's a fun trick to avoid doing trigonometry. You can do it if the program you're designing your board in has a circle or arc tool, or if you are making a drawing on paper with a compass and a straightedge.



Be careful with this technique, you can accidentally discover the secrets of the universe.
JakoGreyshire
Funny thing about the universe secrets... hihi
Bodo1967
diode_destroyer wrote:
(In whatever units your original numbers are in, e.g. mm.)


That looks like a PCB template for a 1/4 inch jack - one of those:



So yes, mm should be the correct unit.
whoop_john
If what you are trying to do is place that pin in a PCB program, I usually deal with it by placing a temporary pin at the rotation point and group it with the pin I want to rotate, placed on one of the cardinal points. Then I can rotate the grouped pair by 45º by clicking on the temporary pin, ungroup and delete the temporary pin. It works for me, quicker to do than explain, but I use Osmond PCB on the Mac, so I don't know if other programs will do similar things.

You could probably eyes... it well enough by drawing a circle of the correct radius and a 45º line from the centre. Where they cross is your pin location.
butter
Can also do it with geometry and some algebra...

A 45degree segment is the diagonal of a square, so we know that the horizontal and vertical co-ordinates should be equal lengths (being 2 sides of a square).

So we have pythagoras':
h^2=x^2+y^2
but x=y here, so
h^2=2x^2
42.25=2x^2
21.125=x^2
x=4.59619407771
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