Take a look at the applet
The graph of the function $g\left(x\right)=a\cdot sin\left(b\right(x+c\left)\right)+d$ is a sinusoid. That is a graph that results when you transform the graph of a standard sine function $f\left(x\right)=sin\left(x\right)$ . The graph of $g$ has the following properties:
the amplitude (maximum deviation from the equilibrium) is $a$ ;
the period is $\frac{2\pi}{b}$ so $b=\frac{2\pi}{\text{period}}$ ;
the horizontal translation is $\mathrm{-}c$ ;
the equilibrium is the line $y=d$ .
Take a look at the following applet:
The graph of the function $g\left(x\right)=a\cdot cos\left(b\right(x+c\left)\right)+d$ is a sinusoid. That is a graph that results when you transform the graph of a standard cosine function $f\left(x\right)=cos\left(x\right)$ . The graph of $g$ has the following properties :
the amplitude ( maximum deviation from the equilibrium ) is $a$ ;
the period is $\frac{2\pi}{b}$ so $b=\frac{2\pi}{\text{period}}$ ;
the horizontal translation is $\mathrm{-}c$ ;
the equilibrium is the line $y=d$ .