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.