04.19.2019: One Lesson of Math – Circular Functions, 8/10: Modelling Real Situations Using Sinusoidal Functions

Today’s soundtrack is Dream Theater: Dream Theater, their self-titled album that was the first to feature Mike Mangini writing the drum parts. It’s a great album; though it is a progressive metal album, it isn’t very experimental; in my opinion, that fit the needs of the album well, and it is a very solid effort. I was surprised at the simplicity of the album art; many of their other albums have multi-faceted pieces of art.

This afternoon, I’m learning about ways that we can use trigonometric functions to model real-life situations. Functions whose graph looks like waves are called “sinusoidal functions,” which kind of sounds like it should be a Slipknot song.

Some examples of sinusoidal functions include the sea’s level during tide changes, or temperature changes over the course of a year, etc.

When we are presented with a scenario that could be portrayed as a sinusoidal function, we first sketch it out, then write its equation and graph it.

We can use the “trace” and “value” commands of a graphing calculator to determine various values.