Today I’m conducting an experiment in forethought. For homework I gave my trig students a worksheet with problems they don’t know how to solve (arcsine, arccosine, and arctangent) mixed in with problems they do know how to solve (sine, cosine, and tangent), with the instruction that they were to complete as many of the problems as they knew how. At the top of the page is a list of twenty-six possible solutions, of which fourteen are used. (You can find the worksheet online here like I did.) I hypothesize that two results will come of this.
First, the students will be frustrated about not getting clearer instructions and therefore needing to figure out for themselves which problems to solve.
Second, after seeing sin−1 sandwiched between regular old sin, cos, and tan problems with a list of possible answers, the students will come to class tomorrow with ideas about what sin−1 means . Some may go beyond having an idea and may understand it quite well. If so, my experiment will have been a success by allowing a little forethought on the part of the students to ease the introduction of a new function.