I'm watching Neso Academy series on Signals and Systems, and in one of the videos the problem is to find $x(t)$ when magnitude and phase plot are given. The plot looks like this:
When he finishes calculation he gets:
$4 + 4cos(3 \omega t+ \dfrac\pi2) + 8cos(4 \omega t- \dfrac\pi2)$
I understand the steps that are required to get this, but I don't understand why is it cosine? When you look at magnitude plot you have just 3 components: DC offset = 4 and 2 harmonics.
As far as I know the values on magnitude plot represent sine value and phase plot represents just phase shift of that sine wave. Without doing anything but looking at the plot I would write following:
$4 + 4sin (3 \omega t+ \dfrac\pi2) + 8 sin(4wt-\dfrac\pi2)$
And it's completely wrong, why is it so?
BTW link to the video.