Different amplitude in time-domain vs frequency-domain Reading the book Understanding Digital Signal Processing I am confused with the following picture: 

First figure is the input signal ($x_1(n) = \sin(2\pi f_0nt_s)$, $f_0$ frequency, $t_s$ being the sampling period) at 1Hz. Second is the input signal squared ($y_1(n) = \sin(2\pi f_0nt_s) \cdot \sin(2\pi f_0nt_s)$). Third figure is the second signal displayed in frequency domain. How can it be that the amplitude is $-0.5$ when the second figure is strictly positive and the amplitude is $1$?

Note: I am a complete beginner at this.
How can it be that the amplitude is −0.5


Primarily sloppy notation in the book.

The frequency domain representation of a signal uses complex numbers, i.e. you would need two real numbers to describe it. Either Amplitude and Phase or Real and Imaginary Part. The correct way to describe this would 


Amplitude is $0.5$ and the phase is $\pi$, or
Real part is $-0.5$ and the Imaginary part is $0$


The whole notion of negative/positive doesn't make sense for a complex number, so you can't think about this that way.