Question

Unit circle?
I am asked to find the exact value of the composite function.
Tan^-1(tan 4pi/5).
I understand that for an inverse function, I need to find a value that is within the interval -pi/2 and pi/2.
4pi/5 does not lie in the interval so I am asked to find an angle that lies in Quadrant II and for whose tangent IS 4pi/5.
I'm confused because I have the unit circle memorized and everything but I don't know how to find reference angles that aren't actually listed on the circle.
They get -pi/5, and I'm not sure how they find a point of reference if both 4pi/4 and -pi/5 aren't even on

Answer 1

\[\tan ^{-1}(\tan \frac{ 4\pi }{ 5 }) \] if that helps anyone visualize this better.

Answer 2

tan function is periodic with period of pi
so tan(4pi/5)=tan(4pi/5-pi)=tan(..?..)

Answer 3

OH. negative 5 over pi.

Answer 4

So you just need to understand the periodic properties of each function, then?

Answer 5

Negative pi over 5, I meant, lol.

Answer 6

yes. sin and cos are periodic with 2pi, tan and cot with pi.
so sin(x +/- 2pi) = sin x
cos(x +/- 2pi) = cos x
tan(x +/- pi) = tan x

Answer 7

Ahh. Thank you sooo much. I understand now. :)

Answer 8

welcome :)