We just finished learning how to solve all sorts of basic trig equations (cos ___ = #, cos # = ____). We'll get to equations soon, but we wanted the students to see some applications right away. I didn't want the standard: Billy is standing 5 feet away from a tree and how tall is the tree problems from geometry.
I searched in my favorite precalculus textbooks for some ideas, and found some applications under the GRAPHING and TRANSFORMING of sine wave functions/equation section. With a bit of fiddling, I adjusted the problems, so that the students could just find the angle or plug in the angle.
We first had a discussion on the cyclic behavior of sine. Then we brainstormed as to what in real life gets bigger then smaller then bigger and on and on. Then I showed them this sheet. We made sure to discuss how in algebra when you are solving for a variable you have to isolate it by undoing what's being done to it. Then I mentioned that this is JUST like solving for "x" in algebra, but on "steroids".
Voila! New problems for the kidlets to tackle: