SOLUTION: Find the exact value of tan 15 degrees

Question 220645: Find the exact value of tan 15 degrees
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the exact value of tan 15
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[tan(15) = tan(60-45)
= [tan(60)-tan(45)]/[1+tan(60)*tan(45)]
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= [sqrt(3)-1]/[1+sqrt(3)*1]
Multiply numerator and denominator by 1-sqrt(3) to get:
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= [-(1-sqrt(3))^2]/(1-3)
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= (1-2sqrt(3)+3)/2
= (4-2sqrt(3)]/2
= (2-sqrt(3))
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Cheers,
Stan H.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
tan (15) = .267949192 by the calculator.
tan (15) = 0.267949192431123 by excel spreadsheet function.
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I don't know if it just stops there or if excel doesn't have the capability to extend the fraction any further.
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For it to be exact, it would have to be the result of the ratio of two integers.
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I would be at a total loss to determine what integers would result in that fraction.
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my guess is that it's probably irrational and so the fraction would go on endlessly without any repeating patterns to indicate that even if it's an endless fraction, it was the result of the ratio of two integers.
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but that's just a guess.
I really don't know.
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