Creating a Graph of the Sine Function
In this lesson, Mary and Claire develop a graph of the sine function. They grapple with how to scale the x- and y-axes so they can show the relationship between an object’s angle of rotation and its height above the midline of a circle as it travels along the circumference of that circle.
Episode 1: Making Sense
The students mark in an object’s height above the midline of a circle at several stops along its circular path. They coordinate these heights with the object’s angle of rotation and mark these in as well.
Episode 2: Exploring
The students attempt to develop a graph that relates the angle of rotation of a fly and its height above the midline as it travels on the blade of a fan in a circular path. They begin by measuring the fly’s heights above the midline at several stops along the its circular path and plotting these heights on a graph.
Episode 3: Exploring
The students revise the graph they created in the previous episode. They plot several points that relate the height of an object above the midline of a circle and its angle of rotation as it moves around a circular path.
Episode 4: Repeating Your Reasoning
Mary and Claire make their graph more accurate by plotting several more points.
Episode 5: Repeating Your Reasoning
Mary and Claire begin to create a graph that relates an object’s angle of rotation, measured in radians, with its height above the midline, measured in radii, as it travels along a circular path.
Episode 6: Reflecting
The students reflect on how to use the sine button on a calculator to find the height of an object at various stops as it travels along a circular path.
Mathematics in this Lesson
Targeted Understandings
Common Core Math Standards
Common Core Math Practices