The GeoGebra mapping diagram visualizes the steps in the algebra for solving equations of the form $f(x)=A*trig(Bx-C)+k=D$ with $A,B \ne 0$ and $trig = \sin, \cos$ or $\tan$.

Comments: You can use the sliders to investigate other examples by $A,B,C$ as well as $k$.

You can move the (red) point labelled D on the right axis of the mapping diagram to change the value of $D$.