SOLUTION: Calculate the exact answer. No decimals. tan((14pi)/3)

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Question 919009: Calculate the exact answer. No decimals.
tan((14pi)/3)
Found 4 solutions by lwsshak3, josmiceli, MathLover1, MathTherapy:
Answer by lwsshak3(11628)   (Show Source):
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Calculate the exact answer. No decimals.
tan((14pi)/3)=4π+(2/3)π=4π+2π/3
tan(2π/3)=sin(2π/3)/cos(2π/3)=-1/0=undefined
tan((14pi)/3) is undefined

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!

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You can step through this:
Note that
is a full 180 degree circle
bringing you back to 0 degrees
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is 2 full
circles which again brings you back to
0 degrees
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Note that
So, that makes the problem:

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This is more than , so the angle is in
the 2nd quadrant where the tan is negative (+)/(-)
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The angle made with the horizontal is ,
which is 60 degrees, so I can say:

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Always do a drawing -it helps

Answer by MathLover1(20855)   (Show Source):
You can put this solution on YOUR website!
is degrees
Draw a triangle with angles , , and .

Opposite the degree angle is .
Adjacent to the degree angle is .

or

is => degree

, so
Opposite the degree angle is .
Adjacent to the degree angle is .
=>

Answer by MathTherapy(10809)   (Show Source):
You can put this solution on YOUR website!
Calculate the exact answer. No decimals.
tan((14pi)/3)

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Reference angle of : 840 - 360 * 2 =
tan is in the 2nd quadrant where sin is POSITIVE, cos is NEGATIVE, and so, tan is NEGATIVE