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... 

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 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 coordinates 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 

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.) 
how to find the coordinates of A,B, i tried the same trick and deduce from X,Y (4.59619), but that didn't work. i did read up on Pythagoras and the Cartesian, but i couldn't find the answer on how to find the second coordinates.
i need to have that line spot on the hole and as wide as specified on the drawing, 2.5 mm or 1.25 mm north west and 1.25 mm "south east"
thnx in advance. 

AnalogFan 
Bodo1967 wrote:  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. 
yes it is
PJ612A 1/4 inch Jacks 

AnalogFan 
ranix wrote:  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. 
thnx, that's how i learned it at school, but the grid in eagle! 

EATyourGUITAR 
North south east and west are depreciated in 2 dimensional coordinate systems since they are intended to describe vectors on a spheroid earth in 3 dimensional space. Mathematicians now prefer up down left right or you can use degrees, radians, phase angle, vectors or anything else but not that. 

AnalogFan 
EATyourGUITAR wrote:  North south east and west are depreciated in 2 dimensional coordinate systems since they are intended to describe vectors on a spheroid earth in 3 dimensional space. Mathematicians now prefer up down left right or you can use degrees, radians, phase angle, vectors or anything else but not that. 
thnx, but this type of Maths is rusty and that is what came up in me. 
