[color=#000000]In the applet below, point P lies on the graph of the function y = cosh(x), or y = the hyperbolic cosine of x. [br]The graph of this function is referred to as a catenary. Hanging chains or wires, when left to hang under the influence of gravity, take the shape of a catenary. [br][br]Nonetheless, [/color][color=#980000][b]point [i]D[/i][/b][/color][color=#000000] lies on a curve that is said to be an [/color][color=#980000][b]involute of this catenary. [br][/b][/color][color=#000000]In the applet below, the length of the segment [/color][i][color=#000000]CD[/color][/i][color=#000000] is equal to the length of the arc with endpoints P and A. Segment [i]AD[/i] is kept tangent to the graph of y = cosh(x) as well. [br][br][/color][color=#000000]Drag the white point [/color][i][color=#000000]P[/color][/i][color=#000000] along the hyperbolic cosine curve to trace out its [/color][color=#980000][b]involute[/b][/color][color=#000000]. [br][/color][color=#000000]Does this [/color][color=#980000][b]brown curve[/b][/color][color=#000000] look familiar? If so, describe. [br] [br]Now compare [/color][color=#980000][b]this curve[/b][/color][color=#000000] with the curve you see here: [/color][color=#000000]https://tube.geogebra.org/m/MTVhRfVp[br][/color][color=#000000]Notice anything familiar? Explain. [/color]