How do I find the value of sin 11pi / 6?

1 Answer
Nghi N.
Aug 14, 2015

Find sin ((11pi)/6)

Ans: (-1/2)

Explanation:

Call sin ((11pi)/6) = sin t
cos 2t = cos ((22pi)/6) = cos ((-2pi)/6 + 12(2pi))=
= cos ((-2pi)/6) = cos ((pi)/3) = 1/2
Use trig identity: cos 2t = 1 - 2sin^2 t = 1/2
2sin^2 t = 1 - 1/2 = 1/2
sin^2 t = 1/4
sin ((11pi)/6) = sin t = +- 1/2
Since the arc (11pi)/6) is located in Quadrant IV, only the negative (-1/2) answer is accepted.

NOTE. One better way is using the trig unit circle to directly find the answer --> sin ((11pi)/6) = - sin pi/6 = -1/2, because the question doesn't mandate using the half angles trig identity

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