Hyperbolic Functions

For the moment, just work with the displayed function and the four sliders in the bottom left corner. How do the fours sliders affect the graph? Since the circle isn't a function, it has been graphed parametrically. Which trig function goes with the $ x $-coordinate of a given point and which one goes with the $ y $-coordinate? Now click on the empty circle by the second parametric equation to display it. How do the sliders affect this shape? What names does this graph suggest for our two new functions?