Example  TRIG.DSEQ.0.  Dynamic Views for solving a trigonometric equation:
$f(x) = A\ trig (Bx+C) + k = D$ with $A, B \ne 0$ and $trig = \sin, \cos$ or $tan$ on Graphs and Mapping Diagrams.

Comment: The problem can be restated: to find a $x$ where $f(x) = D$. This problem and its solution can be visualized both on the graph and the mapping diagram for the function $f$.

Comments: You can move the (red) point labelled x on the left axis of the mapping diagram to a position where the arrow head points to $f(x) = D$ and the corresponding point on the graph of $f$  will move to the position where the graph of $f$ crosses the line $y = D$.
Check the box and the diagram will show the solution on both the mapping diagram and the graph.

You can use the sliders to investigate sine, cosine, or tangent and other examples by $A,B,C,k$, as well as $D$.
Visualization of Solutions with Mapping Diagram Connected to Algebra.

Comments: You can move the (red) point labelled x on the left axis of the mapping diagram to a position where the arrow head points to $f(x) = D$ and the corresponding point on the graph of $f$  will move to the position where the graph of $f$ crosses the line $y = D$.
Check the box to see the first algebraic step to solving the equation and continue to see the steps through to the final solution. At each step the diagram will show the solution step visualized on the mapping diagram.

You can use the sliders to investigate sine, cosine, or tangent and other examples by $A,B,C,k$, as well as $D$.