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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: $\text{A.}\ t= \frac{317\pi}{4}$ $317\left(\frac\pi4\right)$ $\frac\pi4= \frac18\left(2\pi\right)$ $\Rightarrow t= \frac{317\pi}{4}$ is on the same spot as $\frac\pi4$, in QI. $\text{B.}\ t= -\frac{19\pi}{6}$ $-\frac\pi6= \frac13\left(-\frac\pi2\right)$ This means $t= -\frac{19\pi}{6}$ is a third between$\frac{3\pi}{2}$ and $2\pi$.
 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 $\text{A. }\frac{317\pi}{4}\,=\,79\frac14\pi\,\Rightarrow\,\ pi\,+\,\frac{\pi}{4}\,=\,\frac{5\pi}{4}$ $\text{B. }-\frac{19\pi}{6}\,=\,-3\frac16\pi\,\Rightarrow\,\pi\,-\,\frac{\pi}{6}\,=\,\frac{5\pi}{6}$
May 6th, 2013, 07:40 PM   #3
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Re: Points on unit circle

Quote:
 Originally Posted by greg1313 $\text{A. }\frac{317\pi}{4}\,=\,79\frac14\pi\,\Rightarrow\,\ pi\,+\,\frac{\pi}{4}\,=\,\frac{5\pi}{4}$
$\text{What's the reasoning at this point: 79\frac14\pi?}$

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 thirty-nine and one-half rotations on the unit circle. This leaves us at pi, then we add a quarter.
May 7th, 2013, 02:46 AM   #5
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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:
 Originally Posted by greg1313 79 is an odd number, so we complete thirty-nine and one-half rotations on the unit circle. This leaves us at pi, then we add a quarter.
Do you mean seventy-nine instead of thirty-nine?
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
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Re: Points on unit circle

Quote:
 Originally Posted by Aftermath 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.
Try 319?/4.

May 9th, 2013, 11:15 AM   #8
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Re: Points on unit circle

Quote:
Originally Posted by greg1313
Quote:
 Originally Posted by Aftermath 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.
Try 319?/4.
Sorry for the delay in reply. Thanks for your responses so far!

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.

$\frac{319\pi}{4}= 79 \frac{3\pi}{4} = \pi + \frac{3\pi}{4} = \frac{7\pi}{4}$

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
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Re: Points on unit circle

Quote:
 Originally Posted by Aftermath 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. $\frac{319\pi}{4}= 79 \frac{3\pi}{4} = \pi + \frac{3\pi}{4} = \frac{7\pi}{4}$

Quote:
 Originally Posted by Aftermath 79? is the same as 2(39?).

May 9th, 2013, 12:27 PM   #10
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Re: Points on unit circle

Quote:
Originally Posted by greg1313
Quote:
 Originally Posted by Aftermath 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. $\frac{319\pi}{4}= 79 \frac{3\pi}{4} = \pi + \frac{3\pi}{4} = \frac{7\pi}{4}$

Quote:
Originally Posted by greg1313
Quote:
 Originally Posted by Aftermath 79? is the same as 2(39?).
I'm wrong. 79? is the same as 2(39.5?)

Thank you very much for your patient help!

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