Why is this answer zero

using coterminal angles, find exact values of each expression, no calculator

tan(21pi). Please explain as if you were teaching me, i don't really get these concepts.

Everything including and larger than 2π is redundant, you're just transversing the circle more than one time which makes no difference when evaluating as we only care about where we end. So start taking off circles.
tan(21π) = tan(21π - 2π) = tan(19π) = tan(19π - 2π) = tan(17π) = ...
= tan(3π - 2π) = tan(π)

Then tangent is defined as the ratio of sine and cosine, so
tan(π) = sin(π) / cos(π)

and if you take a look at the unit circle you'll see that this is
0 / 1 = 0

If you look at a unit circle (click below to view one):

http://math.rice.edu/~pcmi/sphere/drg_tx…

you will see that 0 radians is the same as 2π, is the same as 4π, ... , is the same as 2nπ radians, and also, you will see that π radians is the same as 3π radians, is the same as ... (2n-1)π radians.

21π, which is (2[11] -1)π radians, is the same as π radians.

If you look up the value of tan(π) on a chart of trig values for special angles (click below), you will see than tan(π) = 0. Therefore, tan(21π) = tan(π) = 0.

http://sites.csn.edu/istewart/mathweb/ma…

And there ya have it!
alice

tan (21pi) = tan (21 x 3.14) = 65.94 (66 +/-)

Using the tangent tables, tan 66 = 2.2460, so I don't understand why the correct answer is zero.