<PRE><B>Question 113033</B>
I&#39;m going to assume that the 6 holes are to be arranged in a circular pattern with the centers of the holes on a circle with center (0,0) and a radius of 5.5, and that the 6 holes are to be equally spaced around the circle.


The stipulation that the first hole is &#39;on top of&#39; the y-axis means, to me, that the center point of the first hole lies on the y-axis.  Given that, your presumption that the first hole is located at (0,5.5) is correct.


Since we know that there are {{{2*pi}}} radians in a circle, and we have to space 6 holes equally, the angle between the radii connecting the origin to the centers of any two adjacent holes must be {{{pi/3}}} radians {{{(2*pi)/6}}}.


So, in polar coordinates (r, a) where r is the radius and a is the angle the radius makes with the x-axis, the six holes are positioned at:


Hole 1: (5.5,{{{pi/2}}})
Hole 2: (5.5,{{{5*pi/6}}}), (going counter-clockwise)
Hole 3: (5.5,{{{7*pi/6}}}),
Hole 4: (5.5,{{{3*pi/2}}}),
Hole 5: (5.5,{{{11*pi/6}}}), and
Hole 6: (5.5,{{{pi/6}}})


To convert from polar to rectangular coordinates, which is what you are looking for, use {{{x=r*cos(alpha)}}} and {{{y=r*sin(alpha)}}}


Fortunately for ease of calculation, all of these angles are multiples of 30 degrees, and we can use our knowledge of the relationships between the sides of  30-60-90 triangle to give us the appropriate sin and cos values.


Hole 1:  {{{x=5.5*cos(pi/2)=0}}}, {{{y=5.5*sin(pi/2)=5.5}}}
Hole 2:  {{{x=5.5*cos(5*pi/6)=5.5*(-sqrt(3)/2)}}},  {{{y=5.5*sin(5*pi/6)=5.5*(1/2))}}}
Hole 3:  {{{x=5.5*cos(7*pi/6)=5.5*(-sqrt(3)/2)}}},  {{{y=5.5*sin(7*pi/6)=5.5*(-1/2))}}}
Hole 4:  {{{x=5.5*cos(3*pi/2)=0}}}, {{{y=5.5*sin(3*pi/2)=-5.5}}}
Hole 5:  {{{x=5.5*cos(11*pi/6)=5.5*(sqrt(3)/2)}}},  {{{y=5.5*sin(11*pi/6)=5.5*(-1/2))}}}
Hole 6:  {{{x=5.5*cos(pi/6)=5.5*(sqrt(3)/2)}}},  {{{y=5.5*sin(pi/6)=5.5*(1/2))}}}


I&#39;ll let you do the arithmetic because you didn&#39;t specify an accuracy tolerance.  But be VERY careful with the signs.

Hole 1 is on the axis between quadrant I and II, so x = 0 and y is +
Hole 2 is in the II quadrant, so x is - and y is +
Hole 3 is in the III quadrant, so x is - and y is -
Hole 4 is on the axis between quadrant III and IV, so x = 0 and y is -
Hole 5 is in the IV quadrant, so x is + and y is -
Hole 6 is in the I quadrant, so x is + and y is +


Hope this helps,
John</PRE>