#arctan " or " tan^(-1)# are both the same thing.
Tangent is the numeric value you obtain if you have #("opposite")/("adjacent")# for a right triangle. In other words the amount of 'up' for 1 'along'. It is the gradient value of the hypotenuse
Ok! we have now established what a tangent is so what is #tan^(-1)#? Put simply it is the process of reversing the numeric tangent value back into the angle between the hypotenuse and the adjacent.
#tan(3 pi/5)# converts the angle of #3 pi/5# into the gradient.
#tan^(-1) " of " tan(3 pi/5)# reverses the process. So if you have
#tan^(-1)(tan("something")# the #tan^(-1)(tan()# cancel each other out and you are left with just the angle that you started with.
so #tan^(-1) (tan(3 pi/5)) =3 pi/5#
