Trigonometric Equation Exploration

Create a diagram for exploring a trigonometric equation graphically: include five adjustable input fields for equation-related parameters, then define a curve or line used to find an intersection with it. Compute and display the intersection point with the reference coordinate given in the prompt, and add a text label showing the form of the intersection’s x-coordinate divided by π. Also incorporate a mode/selection control determined by one of the constructed objects, and display a message indicating whether the chosen object has zero length (use one message when it is zero and another when it is nonzero, reflecting the possibility of repeated digits). Finally, draw a vertical segment whose x-position is shifted by a difference of two inputs and whose top endpoint depends on a computed height from the inputs, following the order of inputs → intersection → text annotation → segment → conditional message.