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 
