This is the first of two lessons in which students explore the unit circle, defined as a circle of radius 1 and centered at the origin. They focus first on the symmetric nature of the coordinates of points on the unit circle and then learn that these points can also be defined by their angle of rotation, which leads to working with radian angle measurements as students increase the precision of language in describing the location of a point on the unit circle (MP6).

Students recall that 1 radian is the angle when the length of the arc that the angle intersects, on a circle of radius , is . Because is the ratio of the circumference of the circle to its diameter, there are radians in a full circle. This lesson includes an optional activity if students need practice recalling the definition of radian measurement.

Students look for regularity in repeated reasoning as they apply radian measure to examine the distance that a wheel travels as it rolls for several angles, reasoning that the measure of the angle of revolution corresponds to the distance traveled when the radius is 1 (MP8).