Sinusoids

• ``Sinusoids'' is a collective term referring to both sine and cosine functions.
• A sinusoid is a function having the following form:
  $$x(t) = A\sin(\omega t + \phi)$$   or$$\quad x(t) = A\cos(\omega t + \phi),$$
  where $x$ is the quantity which varies over time and
  

  $$A \triangleq$$ peak amplitude

  $$\omega \triangleq = 2\pi f$$

  $$f \triangleq$$ frequency (Hz)

  $$t \triangleq$$ time (seconds)

  $$\phi \triangleq$$ initial phase (radians)

  $$\omega t +\phi \triangleq$$ instantaneous phase (radians)

  
  

Figure 1: Sinusoid where $A=2$, $\omega = 2\pi 5$, and $\phi = \pi /4$.