# Day 77: Multiple Representations for Trig Equations

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.