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 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.

  How this lesson came about
  Problem-based Approaches: How this lesson came about
Loading resource...

Introduction to Trigonometric Functions and their Graphs

Unit 12: Unit Circle Trigonmetry
Lesson 5 of 5

Objective: SWBAT explain how a trigonometric function models a situation.

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

  Print Lesson
1 teacher likes this lesson
Similar Lessons
What do Triangles have to do with Circles?
Algebra II » Trigonometric Functions
Big Idea: How is the unit circle related to "triangle measurement"? A story of two equivalent definitions.
Fort Collins, CO
Environment: Suburban
Jacob Nazeck
Riding a Ferris Wheel - Day 2 of 2
12th Grade Math » Trigonometric Functions
Big Idea: Make the transition from the Ferris wheel problem to the unit circle.
Troy, MI
Environment: Suburban
Tim  Marley
Investigating Radians
12th Grade Math » Rotations and Cyclical Functions
Big Idea: Students use cylinders and string to investigate radian angle measurements and then use their findings to develop a method to convert from radian to degrees.
Phoenix, AZ
Environment: Urban
Tiffany Dawdy
Something went wrong. See details for more info
Nothing to upload