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

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(24713) (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 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 radians .

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,)
Hole 2: (5.5,), (going counter-clockwise)
Hole 3: (5.5,),
Hole 4: (5.5,),
Hole 5: (5.5,), and
Hole 6: (5.5,)

To convert from polar to rectangular coordinates, which is what you are looking for, use and

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: ,
Hole 2: ,
Hole 3: ,
Hole 4: ,
Hole 5: ,
Hole 6: ,

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
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