Question 296613: find the exact value of tan 17pi/12
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the exact value of tan(17pi/12)
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17pi/12 = 17*15 = 255 degrees = -105 degrees
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-105 degrees = -60+(-45) degrees
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tan(-60+(-45)) = [tan(-60)+tan(-45)]/[1-(tan(-60))(tan(-45))]
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tan(-60) = sin(-60)/cos(-60) = (-sqrt(3)/2)/(1/2) = -sqrt(3)
tan(-45) = sin(-45)/cos(-45) = (-sqrt(2)/2)/(sqrt(2)/2) = -1
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So tan(17pi/12) = [-sqrt(3)-1]/[1-(-sqrt(3)(-1)]
= -[1+sqrt(3)]/[1-sqrt(3)]
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Cheers,
Stan H.
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