How do you find the exact value of $sin((14pi)/6)$ ?

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Answer 1 · 2017-01-19T20:21:46

$sin((14pi)/6)=(sqrt(3))/2$

First because $14/6=7/3(2/2)=(7/3)(1)=(7/3)$ , we can say

$sin((14pi)/6)=sin((7pi)/3)$

And since $7/3=(6+1)/3=6/3+1/3=2+1/3$ , we can say

$=sin((2pi+pi/3))=sin(pi/3)=ul((sqrt(3))/2)$

So, we have gone around the unit circle once, and landed at $pi/3$ .

How do you find the exact value of sin((14pi)/6)sin((14pi)/6)?