Question 491735: ALRIGHT, so I understand cos23pi/6 can be solved using the unit circle but I don't thoroughly understand HOW to count it to find the answer. What I mean by this is: do I start on 30 degrees, which is pi/6, and count every 30 degrees until I get to 23? ugh! I'm so confused, PLEASE help me! I will be most grateful toward you!
Found 2 solutions by scott8148, lwsshak3:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! you start at 0º (the positive x-axis)
___ you're only interested in what fraction of a full circle you have to traverse
so any multiples of 2pi (a full circle) can be subtracted
in this case 12pi/6 can be used in place of 2pi
as it turns out, 23pi/6 is just pi/6 short of two full circles
so what you are looking for is cos(-30º) -- a 30º reference angle in the IV quadrant
___ or, if you don't like negative angles, cos(330º)
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! ALRIGHT, so I understand cos23pi/6 can be solved using the unit circle but I don't thoroughly understand HOW to count it to find the answer. What I mean by this is: do I start on 30 degrees, which is pi/6, and count every 30 degrees until I get to 23?
**
The idea here is to find out the reference angle and the quadrant you will end up in. For given problem you can multiply 30º by 23 to get 690º which gives reference angle of 30º in quadrant IV.
..
Another way one might look at it is that starting from zero, for every rotation of 6π, the angle moves 180º, so at 23π the angle will end up at 180º with 5π/6 radians to go which places the angle at 330º in quadrant 4. Divide 23 by 6 to get 3-180º moves with the remainder 5 telling you how much further to go.
Hope this helps.
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