## Reflection: Problem-based Approaches Introduction to Trigonometric Functions and their Graphs - Section 3: Extending the Domain of the Sine Function to all Real Numbers

As I've said before, I teach an Honors Geometry course. One of the extension I decided to do was incorporating unit circle trigonometry. In order to do that, I needed to make the transition from trig ratios (i.e., just something we use to solve right triangles) to trig functions. Not only would that obviously involve the idea of functions generally, but also the specifics of trig functions...in a way that would be palatable to ninth graders.

So as I was thumbing through the book, I came to a problem that asked students to calculate the area of a static parallelogram with given side lengths and the measure of one angle. I thought to myself, "If I make this a dynamic situation, rather than static, I think I'll have my segue from trig ratios to trig functions". And that's where the journey began. Next I had to find a way to represent the problem visually. That's where Sketchpad was useful. Desmos was good for analyzing the function's behavior. And Finally I had to develop some resources that would scaffold the logical sequence for students.

In my mind, this is what it means to be a math teacher at this particular time. It's taking what may have existed before, or possibly never existed, and finding ways to mold it and supplement it in order to effect the learning outcomes that are called for by the CCSS. It's no small challenge and even with the backlash that comes along with it, I'm still glad to be a part of this pioneering effort. As they say, somebody's gotta do it.

Problem-based Approaches: How this lesson came about

# Introduction to Trigonometric Functions and their Graphs

Unit 12: Unit Circle Trigonmetry
Lesson 5 of 5

## Big Idea: It's getting wacky! Angles bigger than 180 and negative areas. What is the world coming to?

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90 minutes

### Anthony Carruthers

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