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what is the exact value of sin(11pi/12)?

trigonometric identities.
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Mina Herzog

Feb 20, 2025

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... Show More
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M
Mina Herzog

Feb 20, 2025

there is a problem.if u write sin(11pi/12)=sin(pi-pi/12) the answer will be (sqrt6+sqrt2)/4.(sqrt is radical)can u explain me why?... Show More
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