Lesson 11

This lesson begins by asking students to make the logical step that negative radians mean rotating clockwise since positive radians mean rotating counterclockwise. Returning to the familiar context of a clock face and the rotation of an hour hand, they use the structure of the unit circle to develop strategies for identifying negative radian measurements (MP7). Next, students create visual displays for the graphs of \(y=\cos(\theta)\) and \(y=\sin(\theta)\) for negative and positive angles, highlighting some important features of the graphs and what those features say about the periodic nature of the functions. In later lessons, they will transform cosine and sine functions to model different situations.

This lesson includes an optional activity that offers students more practice working with the graphs of cosine and sine.

Graphing technology is required for the optional activity “Cosine and Sine Together.”