arctan " or " tan^(-1)arctan or tan−1 are both the same thing.
Tangent is the numeric value you obtain if you have ("opposite")/("adjacent")oppositeadjacent 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)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)tan(3π5) converts the angle of 3 pi/53π5 into the gradient.
tan^(-1) " of " tan(3 pi/5)tan−1 of tan(3π5) reverses the process. So if you have
tan^(-1)(tan("something")tan−1(tan(something) the tan^(-1)(tan()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/5tan−1(tan(3π5))=3π5
