SOLUTION: This is going to be difficult to explain but I will do my best. This is a CNC problem (computer numerical control). It states: Determine X-Y locations for drilling 6 holes. The

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Question 113033: This is going to be difficult to explain but I will do my best. This is a CNC problem (computer numerical control). It states: Determine X-Y locations for drilling 6 holes. The origin or 0,0 point is in the center. The first hole is located on the top of y axis.


Assuming that the radius is 5.50 inches, then the first hole location would be XO, Y 5.50. The second hole location would be 60 degrees from the first. Calculate the X ( ), Y ( ) for each hole.
Please help me I am so lost and confused.
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
I'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 'on top of' 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%2Api 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%2F3 radians %282%2Api%29%2F6.

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%2F2)
Hole 2: (5.5,5%2Api%2F6), (going counter-clockwise)
Hole 3: (5.5,7%2Api%2F6),
Hole 4: (5.5,3%2Api%2F2),
Hole 5: (5.5,11%2Api%2F6), and
Hole 6: (5.5,pi%2F6)

To convert from polar to rectangular coordinates, which is what you are looking for, use x=r%2Acos%28alpha%29 and y=r%2Asin%28alpha%29

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%2Acos%28pi%2F2%29=0, y=5.5%2Asin%28pi%2F2%29=5.5
Hole 2: x=5.5%2Acos%285%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29, y=5.5%2Asin%285%2Api%2F6%29=5.5%2A%281%2F2%29%29
Hole 3: x=5.5%2Acos%287%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29, y=5.5%2Asin%287%2Api%2F6%29=5.5%2A%28-1%2F2%29%29
Hole 4: x=5.5%2Acos%283%2Api%2F2%29=0, y=5.5%2Asin%283%2Api%2F2%29=-5.5
Hole 5: x=5.5%2Acos%2811%2Api%2F6%29=5.5%2A%28sqrt%283%29%2F2%29, y=5.5%2Asin%2811%2Api%2F6%29=5.5%2A%28-1%2F2%29%29
Hole 6: x=5.5%2Acos%28pi%2F6%29=5.5%2A%28sqrt%283%29%2F2%29, y=5.5%2Asin%28pi%2F6%29=5.5%2A%281%2F2%29%29

I'll let you do the arithmetic because you didn'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