what is the exact value of sin(11pi/12)?
What is the exact value of sin(11π/12), and how can trigonometric identities be applied to derive this value?
2 Answers
sin (11π / 12) = sin (3π/12 + 8π/12)
= sin (π/4 + 2π/3)
= sin π/4 . cos 2π/3 + cos π/4 . sin 2π/3 [because sin(a + b) = sina cosb + cosa sinb]
= 1/√2 . cos (π – π/3) + 1/√2 . sin (π – π/3)
= 1/√2 . (-cos π/3) + 1/√2 . sin π/3
= 1/√2 . (-1/2) + 1/√2 . √3 /2
= √2 /2 . (-1/2) + √2 /2 . √3 /2 [Rationalizing the denominators]
= -√2 / 4 + √6 / 4
= (√6 – √2) / 4
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