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May 6th, 2013, 02:56 AM  #1 
Member Joined: Mar 2013 Posts: 36 Thanks: 0  Points on unit circle
Hello. Find the point P(t) on the unit circle for the values below: is on the same spot as , in QI. This means is a third between and . 
May 6th, 2013, 05:30 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Points on unit circle 
May 6th, 2013, 07:40 PM  #3  
Member Joined: Mar 2013 Posts: 36 Thanks: 0  Re: Points on unit circle Quote:
I'm guessing the ? + ?/4 has something to with the reference angle, although I'm not sure exactly what?!  
May 7th, 2013, 02:11 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Points on unit circle
79 is an odd number, so we complete thirtynine and onehalf rotations on the unit circle. This leaves us at pi, then we add a quarter.

May 7th, 2013, 02:46 AM  #5  
Member Joined: Mar 2013 Posts: 36 Thanks: 0  Re: Points on unit circle
I think I'm getting it. The 317 frightened me. Since 317 is odd and the radian measure is ?/4, we simply start at ?. And since 317?/4 is positive it goes in the counterclockwise direction from ?, ?/4 units to give 5?/4. Quote:
Where did the 79 come from? It isn't a factor of 317; I'm guessing that you chose it randomly because it is odd?!  
May 7th, 2013, 03:00 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Points on unit circle
317/4 = 79 + 1/4. This is a factor of pi. Dividing 79 by 2 we obtain 39 complete rotations around the unit circle, with a remainder of 1/2. This leaves us at pi. Then we add 1/4. For clarification, consider 2?. It is one complete rotation around the unit circle. 
May 7th, 2013, 03:28 AM  #7  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Points on unit circle Quote:
 
May 9th, 2013, 11:15 AM  #8  
Member Joined: Mar 2013 Posts: 36 Thanks: 0  Re: Points on unit circle Quote:
319/4 is 79 + 3/4. From this we are going around the circle 39 and a half times. Landing back on ?. Now add the 3/4 to get 7?/4. I got the point about 2? as it relates to 39. 79? is the same as 2(39?).  
May 9th, 2013, 11:24 AM  #9  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Points on unit circle Quote:
Quote:
 
May 9th, 2013, 12:27 PM  #10  
Member Joined: Mar 2013 Posts: 36 Thanks: 0  Re: Points on unit circle Quote:
Thank you very much for your patient help!  

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