Question

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

Answer 1

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

Explanation:

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`.