This lesson invites students to consider the need for a new type of function in which the output values of the function repeat at regular intervals. The term period is introduced and linked to circular motion, using the idea of the motion of the hands of a clock, a context that students will revisit throughout the unit as they make sense of periodic functions (MP1). 

Students reason abstractly and quantitatively as they assign coordinate values to points on a clock hand (MP2). In the following lessons, students build on the foundational work of this lesson as they use trigonometry to identify coordinates of points on a circle and establish the Pythagorean Identity and the unit circle.