Work on the secant curve in the workspace below, so you don't confuse the secant and the tangent curves.
To create a trace of the secant curve, you'll need to use the same set up as the tangent curve.
Use the Ray tool to create a ray from the center B to the rotating point A, the hypotenuse of your triangle.
Enter and , the adjacent sides of your unit triangles. Create a point D at the intersection of ray BA and x=1, and then slide to rotate point A so you can create a point E at the intersection of ray BA and x=-1.
Since , the length of the hypotenuse in the unit triangle will be the output of the secant curve. The length of the hypotenuse is not a coordinate of the points on the unit circle, so we can't use the method we used in the tangent curve.
Click the gray circle next to Ray(B,A) on the list to the left to remove the ray from the diagram. Use the Segment tool to create a segment from point B to E. The length of the segment should show up in the list to the left as 'i : Segment (B,E)'. If your segment shows up as a letter other than 'i', that's fine.
Move the slider for back so you that point D shows up again. Use the Segment tool to make a segment from B to D.
Create a point by entering and turn on the trace for the point. Move the slider for back so that point E shows up again. Create a point by entering and turn on the trace for the point.
Press play on the slider for .