These are challenging, multi-step applications of inverse trig functions. Students analyze rates of change within inverse trig functions, and find a composite function (inverse trig of a linear or quadratic function). There are three different problems that will each take at least a full class periods to solve. I suggest dividing the class into groups, giving each group one problem, then having students present their work as a gallery walk on the second day of the lesson. This lesson was designed for an advanced level of PreCalculus (10th and 11th grade students who would take AP Calculus AB during the following school year). I also gave suggestions for further research or consideration at the end of each problem.