Sinusoidal Wave Terminology
It is usually called DC offset or DC component. Since you use $t$ as a variable, which suggests "time", the quantity $b$ would normally be called frequency. Also note that $c$ is not the phase but a time offset. The phase $\phi$ is usually defined as in

$$x(t)=A\sin(2\pi ft+\phi)\tag{1}$$

Comparing (1) to your formula gives $\phi=-2\pi bc$.