I really like the simplicity of this One or Negative One? Trig Identities Task that I found in the 8th Edition of Demana and Waits’ Pre-Calculus Textbook (Section 5.1). That’s why I decided to turn it into a worksheet!
Trig identities are one of my favorite topics to teach in Pre-Calculus. To me, they are a puzzle, and I try to present them to students as a puzzle.
In this activity, students are given five trigonometric expressions. Using trig identities, each expression can be simplified to either 1 or -1. Often when I teach students to simplify trigonometric expressions, they struggle to know when the expression is simplified “enough.” I like this activity since they have a target to aim for (1 or -1), but I haven’t told them the exact target like I do when we prove trig identities.
I did have a few students who just wanted to randomly write down 1 or -1 for each problem… They were a bit annoyed when I told them they had to justify their answers!