What does this sine wave say exactly?

Question

I am currently starting to learn about sine waves and I was just wondering why this sine waves amplitude is the way it is? Like why exactly does it start at 2, peak at negative 1 and peak at 3 instead of starting at 0, peaking at positive then negative 2? id assume it starts just above 2 because its offset from 0 by a certain degrees?Demodulator signal

Answer 1

The most general "sine wave" is $y=y_0+A\sin(2\pi f(x-x_0))$, where $y$ obtains its mean value $y_0$ at $x=x_0$, but in general fluctuates around this mean with amplitude $A>0$, frequency $f$. Two pernickety points:

• We can impose $A>0$ because $A\mapsto-A,\,x_0\mapsto x_0+1/(2f)$ preserves $y$;
• We call $f$ the linear frequency, while $\omega:=2\pi f$ is the circular frequency. You'll often see the sine's argument written as $\omega x-\phi$ with $\phi:=\omega x_0$.

The sine function is $x_0=y_0=0,\,A=\omega=1$.