SOLUTION: if sin π/3 = √3\2 Cos π/3 = 1/2 Sin π/4 = cos π/4 =√2/2 Evaluate without the use of an calculator the exact value of cos 7π/12 I tri

Algebra ->  Trigonometry-basics -> SOLUTION: if sin π/3 = √3\2 Cos π/3 = 1/2 Sin π/4 = cos π/4 =√2/2 Evaluate without the use of an calculator the exact value of cos 7π/12 I tri      Log On


   

Question 972724: if sin π/3 = √3\2
Cos π/3 = 1/2
Sin π/4 = cos π/4 =√2/2
Evaluate without the use of an calculator the exact value of cos 7π/12
I tried using the l.c.m to get 4√3/2 but then I got lost
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if sin π/3 = √3\2
Cos π/3 = 1/2
Sin π/4 = cos π/4 =√2/2
Evaluate without the use of an calculator the exact value of cos 7π/12
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Note:: 7pi/12 = 3pi/12 + 4pi/12 = pi/4 + pi/3
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Your Problem::
cos(7pi/12) = cos[(pi/4)+(pi/3)]
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= cos(pi/4)cos(pi/3)-sin(pi/4)sin(pi/3)
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= (1/sqrt(2))(1/2) - (1/sqrt(2))sqrt(3)/2
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= [sqrt(2)/4] - [sqrt(6)/4]
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= [sqrt(2) - sqrt(6)]/4
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Cheers,
Stan H.