SWBAT to model a situation using sinusoidal curves.

A fun biorhythm problem provides students with practice modeling a sine transformation that includes period changes without a shift.

10 minutes

For the first 10 minutes of class, I will have students take their Homework Quiz #7-8 for the week which is over worksheets #7-8. The electronic version of the quiz is in the Homework Quiz.

35 minutes

As students complete their homework quiz, they will begin working on the handout Student Worksheet - One of Those Days. Today’s activity has students study biorhythm cycles as a context to use trigonometric modeling. My students are usually interested in this topic. Many wonder if it is true (it’s just a theory). Their interest in the topic definitely helps increase their motivation to complete the assignment.

I expect some of my students to struggle a bit with finding their current position according to their personal biorhythmic cycles (see Question 3). In response, I will point out the fact that the first number that students calculate is the number of days they have been alive. Once this idea is established, most students understand why they would be adding or subtracting the numbers in Part 3 of the calculation to shift the graph.

When students reach the challenge problem, I will encourage them to use their graphing calculator to model the three functions. I find that students attempting to do this problem by hand do not have the technical skill to work efficiently. Thus, they find this very difficult!

5 minutes

To wrap up today’s lesson, I wanted to review the answers with students to Question 2:

I think it is important that students are able to write a trigonometric function to model this situation at this time. Today, students should be successful at writing an equation without a horizontal or vertical shift so that in tomorrow’s lesson we can build to writing equations that have these shifts.

Tonight I will assign Homework 10 - Trig Functions.doc. This assignment may seem a bit out of order, but it is because it does not need to be completed for a couple more nights. I just want to give students a heads up that they will need to do some data collection before the lesson Modeling Real World Data (Day 1 of 4).