Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?

Question

1710 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-21T02:24:30

#frac{sqrt 6 - sqrt 2}{4}#

#frac{- sqrt 2 - sqrt 6}{4}#

#-2 - sqrt 3#

#a = sin 15º = sin (60 - 45) = sin 60 cos 45 - cos 60 sin 45#

#a = sqrt 3 / 2 sqrt 2 / 2 - 1/2 sqrt 2 / 2 = frac{sqrt 6 - sqrt 2}{4} #

#b = cos frac{11 pi}{12} = - cos frac{pi}{12} = - cos (60º - 45º)#

#b = - cos 60 cos 45 - sin 60 sin 45#

#b = - 1/2 sqrt 2/2 - sqrt 3/2 sqrt 2 /2#

#b = frac{- sqrt 2 - sqrt 6}{4}#

#c = tan 105º = frac{sin 75}{- cos 75} = frac{sin 30 cos 45 + cos 30 sin 45}{-cos 30 cos 45 + sin 30 sin 45}#

#c = frac{sin 30 + cos 30}{sin 30 - cos 30} = frac{1/2 + sqrt 3 / 2}{1/2 - sqrt 3 / 2} = frac{1 + sqrt 3}{1 - sqrt 3} = frac{(1 + sqrt 3)^2}{1 - 3}#