Construction the Sine Function
In the final lesson, Zoe and Gisele work to combine their insights from the N-gon Task and their definition of a radian. Through this work, they are able to identify inflection points on their graph and improve their description of their graph. This lesson concludes with a big reveal… the graph they have constructed and defined important points on is the graph of the sine function!
Episode 1: Repeating Your Reasoning
The students begin by repeating their reasoning on the circle task by reproducing a graph and their description of the relationship between height and distance traveled by a point.
Episode 2: Exploring
Combining what they have learned, Zoe and Gisele discuss the application of radians as a unit for both distance and height on their graph. Then, they identify a point on the circle and label where that point is represented on their graph.
Episode 3: Repeating Your Reasoning
In this episode, Zoe and Gisele repeat their reasoning through further identification of specific points and the quantitative values on their graph.
Episode 4: Repeating Your Reasoning
Extending their thinking, Zoe and Gisele use the Pythagorean Theorem to label a tricky point on their graph.
Episode 5: Reflecting
In conclusion of this unit, Zoe and Gisele reflect on their graph and their graph is revealed to be a function they have seen before! It’s the sine function!