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): You can put this solution on YOUR website!
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!

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

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


-------------------------------
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(10810)   (Show Source): You can put this solution on YOUR website!
Calculate the exact answer. No decimals.
tan((14pi)/3)


___________

Reference angle of : 840 - 360 * 2 = 



tan  is in the 2nd quadrant where sin is POSITIVE, cos is NEGATIVE, and so, tan is NEGATIVE









 

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