In precalculus, we have begun to look at solving trigonometric equations. Yesterday, we developed the general rules for finding solutions for the Big Three trig functions: sin-1x + 2πn, π – sin-1x + 2πn, cos-1x + 2πn, 0 – cos-1x + 2πn, and tan-1x + πn
I am a bit of a stickler as I require students to use the inverse trig function definitions correctly while solving equations. As an opener, students were asked to do the following:
Find all solutions for the equation: sin2x = – ½. Now find the particular solutions in the domain: [1,5]. Verify solutions graphically.
My goal for this problem was to connect the algebraic process of solving the equation to the graphical results; that is, I wanted multiple representations and understanding for what was really happening.. Once again I wanted the conceptual underpinning to be solid as my kiddos practiced equation solving procedures; that is, I didn’t want mindless robots solving equations without thinking about what was really happening.
I also got to use my Mathematical Practices labels! Double score.
As one of the Trig Review Stations, student had to graph a trig function alone with it’s reciprocal function. How boring in and of itself…so decided to have them glue the graph on one side of a pre-cut snowflake (found at Michaels on sale for 99¢) and the initial equation on the other side. Students used a green pen to graph the initial function and a red pen to graph its reciprocal. Nice discussions as my students completed the task, particularly one who remarked that this helped him clarify inverse with reciprocal…yay!!
Aren’t these fun and also decorates my room for wintertime….notice, no snow yet. What are ways that you have used a skill practice experience to do double duty as room decoration?