precalc 15

 

What does this student know? How would you take the kid to the next level?

Thanks to the Ultimate Tina Cardone for her excellent submissions. Her reign of terror over this blog will end soon!

  • It’s clear from the -1.5 for amplitude that the student recognizes that the amplitude is the distance from the maximum value of a periodic function to it’s middle, but that they don’t know that multiplying the sine function by 3 actually increases the original amplitude by the same factor. Maybe they don’t know enough about function transformations yet?

    As for the period, this is probably a vocabulary issue? I normally introduce concepts first using familiar language and then give names to the concepts as necessary from the more formal vocabulary.

  • Maybe it’s better to pose such questions in their entirety, i.e., graph the function first, preferably manually using standard angle values–with no graphing calculator. Otherwise, the question snippet has no context and instead encourages rote memorization of formulas and shortcuts without requiring any true understanding of trig.

    • What I would like is for students to realize on their own that graphing the function is a useful approach.