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All pi over 6's will always have a numerator that is less than (11 pi over 6 and 5 pi over 6) or more than (pi over 6 and 7 pi over 6) Than that of the pi over 2 or just pi. Use Eugene's example of the x-coordinate for better visualization. Because all pi over 6's are in the 30 degree angle. Of course, they are either + or - depending on the quadrant.

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45 angles are in the middle. 30 degree angles are towards the x axis. 60 degree angles are towards the y axis. (Eugene)

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45 angles are in the middle. 30 degree angles are towards the x axis. 60 degree angles are towards the y axis. (Eugene)

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[Christian Sanchez] sin(60), cos(60), tan(60)

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[Christian Sanchez] sin(60), cos(60), tan(60)

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These numbers and rads are simple as well because sin will always be the longest side in these, therefore sin will always be radical 3 over 2 and negative depending on its quadrant. Cos will always be the short side and therefore be 1/2 and, as well, negative depending on its quadrant. Tan will always be just rad 3 and, once more, negative depending on its quadrant.

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In the 1st quadrant all the numbers are single numbers

(rene)

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In the 4th quadrant all the numbers are prime

(rene)

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Tan only uses the numbers rad 3, 1, and rad 3 over 3

(rene)

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On the first quadrant nothing is negative. On the second quadrant sine and tangent is negative. On the third quadrant sine and cosine are negative. On the fourth quadrant cosine and tangent is negative. (Eugene)

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On the first quadrant nothing is negative. On the second quadrant sine and tangent is negative. On the third quadrant sine and cosine are negative. On the fourth quadrant cosine and tangent is negative. (Eugene)

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These tangent locations are always going to be zero on the horizontal plane and undefined on the vertical plane due to 0 being divided by 1 equals 0 and 1 divided by 0 equals, well, undefined.

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For the 30 degree angles, all the coordinates are + or - square root of 3/2 and 1/2 (Eugene)

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For the 30 degree angles, all the coordinates are + or - square root of 3/2 and 1/2 (Eugene)

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[Christian Sanchez] Sin(45), Cos(45), Tan(45)

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[Christian Sanchez] Sin(45), Cos(45), Tan(45)

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In these places, all numbers are simple. Both sin and cos are equal to radical 2 over 2 and tangent is equal to 1 because radical 2 over 2 divided by radical 2 over 2 equals 1. All angles with a 45 degree measure(These angles are equal to the pi over 4s) is like this one on each opposite side, but with a negative sign depending on the corresponding quadrant the angle is on.

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The coordinates are reflected on the opposite side of the circle except negative

(rene)

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The only numbers in the coordinates for sine and cosine is  1/2, square root of 3/2, and square root of 2/2 (Eugene)

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The only numbers in the coordinates for sine and cosine is  1/2, square root of 3/2, and square root of 2/2 (Eugene)