To begin class, I ask my students to complete the warm-up on Slide 2 of Solving Trig Equations. I selected this problem so that we can review again how to either factor a trig equation or apply the quadratic formula. I want students to work independently and to get as far as they can without assistance (MP1, MP2). I ask that if students get stuck, they text me their last step.
Up to this point, my students have been successful in applying the quadratic formula to a quadratic trig equation. However, they were confused about how to interpret their solutions. After students complete the warm-up, I will model both methods. First, how to factor this polynomial to get solutions. Then, how to solve using the quadratic formula to get the values of -1/3 and 7; then, to set sine equal to these values and solve the basic trig equations from there.
The results in this problem present a good opportunity to also discuss why this equation would not produce any solutions.
To bring closure to today’s lesson, I will have my students cut out the Trig Equations Puzzle Pieces and glue them on a separate sheet of paper. I like the idea of a puzzle instead of just a worksheet because it builds in an opportunity for review and self-assessment. Do the pieces go together and all match? Then they are right! I think that the visual nature of the puzzle helps kids to recognize patterns and reason about mistakes by considering alternatives.
Assign Trig Equations Homework 8.