SOLUTION: How to find the sin, cos and tan of 19pi/6 using the unit circle.

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Question 615316: How to find the sin, cos and tan of 19pi/6 using the unit circle.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since 2pi+=+%2812pi%29%2F6, %2819pi%29%2F6 would be an %287pi%29%2F6 more than one full circle. So %2819pi%29%2F6 and %287pi%29%2F6 are co-terminal angles and will have the same sin, cos and tan values.

Since pi+=+%286pi%29%2F6, %287pi%29%2F6 is pi%2F6 more than pi. This makes %287pi%29%2F6 (and %2819pi%29%2F6) terminate in the 3rd quadrant with a reference angle of pi%2F6

Since sin%28pi%2F6%29+=+1%2F2 and since sin is negative in the 3rd quadrant, sin%28%287pi%29%2F6%29+=+sin%28%2819pi%29%2F6%29+=+-1%2F2
Since cos%28pi%2F6%29+=+sqrt%283%29%2F2 and since cos is negative in the 3rd quadrant, cos%28%287pi%29%2F6%29+=+cos%28%2819pi%29%2F6%29+=+-sqrt%283%29%2F2
Since tan%28pi%2F6%29+=+%281%2F2%29%2F%28sqrt%283%29%2F2%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3 and since tan is positive in the 3rd quadrant, tan%28%287pi%29%2F6%29+=+tan%28%2819pi%29%2F6%29+=+sqrt%283%29%2F3