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

Jamya White

Jamya White

Answered question

2023-03-14

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

Answer & Explanation

Veronella6nk

Veronella6nk

Beginner2023-03-15Added 6 answers

Call sin ( 11 π 6 ) = sin t
cos 2 t = cos ( 22 π 6 ) = cos ( - 2 π 6 + 12 ( 2 π ) ) =
= cos ( - 2 π 6 ) = cos ( π 3 ) = 1 2
Implement trigonometric identity: cos 2 t = 1 - 2 sin 2 t = 1 2
2 sin 2 t = 1 - 1 2 = 1 2
sin 2 t = 1 4
sin ( 11 π 6 ) = sin t = ± 1 2
Since the arc (11pi)/6) is located in Quadrant IV, only the negative ( - 1 2 ) answer is accepted.
Finding the solution directly using the trig unit circle is a more advantageous approach sin ( 11 π 6 ) = - sin π 6 = - 1 2 , since employing the half angles trig identity is not required by the question

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