How to find the argument of a function?

[znaya]

Homework Statement

For the function ##V(f) = A \tau sinc(f \tau)## in the picture how do you conclude that the argument of ##V(f)## is 0º, +180º or -180º?

Homework Equations

##arg = arctan({\frac{Im}{Re}})##

The Attempt at a Solution

The upper graphic represents the absolute value of the function, right? I understand that being a sinc function the negative parts of the graphic should "jump" to the positive side. I also understand why the function return 0 on k/τ.
Is it correct to think, for example, between 1/τ and 2/τ the sinc function returns negative values but because it needs to shift to the positive values the fase should be negative so that negative times negative = positive?
I'm so sorry if this questions sounds too basic. I'm trying to learn by myself, I'm not attending any classes and I have no one to ask this kind of doubts.
Thanks in advance.

 

[theodoros.mihos]

Write analytical ##sinc()## function and think about ##sin()## that you know much better.

 

[znaya]

##sinc(x) = {\frac{\sin(\pi x)}{\pi x}}##

The ##sin()## is positive between ##-2 \pi## and ##- \pi## and between ##0## and ##\pi## and is negative between ##- \pi## and ##0## and between ##\pi## and ##2 \pi##...

 

[theodoros.mihos]

On your function the argument is ##ft## so ##f=\pi##. What must be ##Α## in your function?

 

[znaya]

##A## represents the amplitude of the function, the value that the function return when ##x = 0##

 

[theodoros.mihos]

I think ##A## has only a sign. The second diagram is a step function. Make some diagrams.