Answer:
(β2 - β6) / 4
C. square root of two minus square root of six divided by four.
Step-by-step explanation:
sine of negative eleven pi divided by twelve.
We have :
sin(-11Ο/12)
sin((4 - 15)Ο / 12) = sin(4Ο/12 - 15Ο/12)
sin(4Ο/12 - 15Ο/12) = sin(Ο/3 - 5Ο/4)
Recall:
Angle difference formula:
sin(A - B) = sinAcosB - sinBcosA
Hence,
sin(Ο/3 - 5Ο/4) = sin(Ο/3) cos(5Ο/4) β sin(5Ο/4) cos(Ο/3)
From trigonometry:
sinΟ/3 = β3/2
cos5Ο/4 = -β2/2
sin5Ο/4 = -β2/2
cos Ο/3 = 1/2
(β3/2) (-β2/2) β (-β2/2) (1/2)
-β6/4 - -β2/4
-β6/4 + β2/4
β2/4 - β6/4
(β2 - β6) / 4