I was wondering if someone could please explain to me what this means: the function tan^-1(x) or arctan(x) is a periodical function with the period of pie = 180(degrees)

 

an analogy etc might be useful to me, thanks.

It would be best to look at a graph. If it is periodical over a period, that means it repeats itself. Like a sine wave goes all the way around and back to its starting point in a period of 2π.

Periodic means some function f obeys [math]f(x) = f(x \pm nm)[/math] for any integer n and some value m. The function has the same value when you increase or decrease the input by nm.

 

Arctan isn't periodic, though.

 

Sine and cosine are, though: [math]\sin (x) = \sin (x \pm 2 \pi n )[/math]

im still not sure that i completely understand. but what exactly does the arc (at the start) mean / imply ..?

arc tan means the inverse of tangent.

So, tan (45 degree) = 1.

Arctan (1) =45 degrees.

 

It's a particularly stupid bit of nomenclature

im still not sure that i completely understand. but what exactly does the arc (at the start) mean / imply ..?

 

In radians the angle is associated with the arc length of an arc at radius 1 subtended by the angle. So arctan is the arc, or angle, that produces some value for the tangent function -- the inverse. Since tan is pi periodic, the inverse is only defined modulo pi. arctan is the inverse of tan restricted to (-pi/2, pi/2).