document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113033>Question 113033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Please help me I am so lost and confused.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82348 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Since we know that there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Api%29%2F6 ALIGN=MIDDLE  ALT=\"%282%2Api%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "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:\r<BR>\n" );
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document.write( "Hole 1: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Hole 2: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Api%2F6 ALIGN=MIDDLE  ALT=\"5%2Api%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (going counter-clockwise)<BR>\n" );
document.write( "Hole 3: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Api%2F6 ALIGN=MIDDLE  ALT=\"7%2Api%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >),<BR>\n" );
document.write( "Hole 4: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Api%2F2 ALIGN=MIDDLE  ALT=\"3%2Api%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >),<BR>\n" );
document.write( "Hole 5: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2Api%2F6 ALIGN=MIDDLE  ALT=\"11%2Api%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and<BR>\n" );
document.write( "Hole 6: (5.5,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "To convert from polar to rectangular coordinates, which is what you are looking for, use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=r%2Acos%28alpha%29 ALIGN=MIDDLE  ALT=\"x=r%2Acos%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=r%2Asin%28alpha%29 ALIGN=MIDDLE  ALT=\"y=r%2Asin%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Hole 1:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%28pi%2F2%29=0 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%28pi%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%28pi%2F2%29=5.5 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%28pi%2F2%29=5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hole 2:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%285%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%285%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%285%2Api%2F6%29=5.5%2A%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%285%2Api%2F6%29=5.5%2A%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hole 3:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%287%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%287%2Api%2F6%29=5.5%2A%28-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%287%2Api%2F6%29=5.5%2A%28-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%287%2Api%2F6%29=5.5%2A%28-1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hole 4:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%283%2Api%2F2%29=0 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%283%2Api%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%283%2Api%2F2%29=-5.5 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%283%2Api%2F2%29=-5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hole 5:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%2811%2Api%2F6%29=5.5%2A%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%2811%2Api%2F6%29=5.5%2A%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%2811%2Api%2F6%29=5.5%2A%28-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%2811%2Api%2F6%29=5.5%2A%28-1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hole 6:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.5%2Acos%28pi%2F6%29=5.5%2A%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=5.5%2Acos%28pi%2F6%29=5.5%2A%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5.5%2Asin%28pi%2F6%29=5.5%2A%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"y=5.5%2Asin%28pi%2F6%29=5.5%2A%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'll let you do the arithmetic because you didn't specify an accuracy tolerance.  But be VERY careful with the signs.\r<BR>\n" );
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document.write( "Hole 1 is on the axis between quadrant I and II, so x = 0 and y is +<BR>\n" );
document.write( "Hole 2 is in the II quadrant, so x is - and y is +<BR>\n" );
document.write( "Hole 3 is in the III quadrant, so x is - and y is -<BR>\n" );
document.write( "Hole 4 is on the axis between quadrant III and IV, so x = 0 and y is -<BR>\n" );
document.write( "Hole 5 is in the IV quadrant, so x is + and y is -<BR>\n" );
document.write( "Hole 6 is in the I quadrant, so x is + and y is +\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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