Question

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

Answer 1

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