Example  SEQ.SC.4.  Suppose $4*\sin(2x-1)+1=3$. Find $x$.
Solution: Since $ A \ne 0$ and $B=2, C=-1$, the equation can be solved with $2x-1 =\arcsin \frac D A$  where $A=4,B=2,$ and $D=2$. So the key solution is $ x =\frac 12(\arcsin( \frac 2{4})+1) =\frac 12( \arcsin (\frac 12)+1)= \frac{\pi}{12}+ \frac 12 \approx 0.76$

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 $D$.