Is this the basic building block for any sinusoid function, or for just a Fourier series?
motoole2
This is the building block for any periodic signal. That is, any signal can be expressed as some linear combination of $A \sin(\omega x + \phi)$.
While the Fourier series itself is described as a combination of complex exponentials of the form $a e^{i\omega x}$, note that its real component, $\text{Re}(a e^{i\omega x})$, can be expressed as $A \sin(\omega x + \phi)$, where the values of $A$ and $\phi$ depend on the complex number $a$.
Is this the basic building block for any sinusoid function, or for just a Fourier series?
This is the building block for any periodic signal. That is, any signal can be expressed as some linear combination of $A \sin(\omega x + \phi)$.
While the Fourier series itself is described as a combination of complex exponentials of the form $a e^{i\omega x}$, note that its real component, $\text{Re}(a e^{i\omega x})$, can be expressed as $A \sin(\omega x + \phi)$, where the values of $A$ and $\phi$ depend on the complex number $a$.