This is the first of two lessons focusing on the Pythagorean Identity. 

In this lesson, students recall that for any point  in the first quadrant, whose distance from the origin is 1 unit, the coordinates of the point can be written as the cosine and sine of the radian angle corresponding to point .

Next, students expand this understanding to the other quadrants, viewing cosine and sine as coordinates of a point on the unit circle rather than as lengths of right triangle sides. This is an important transition step as students progress toward thinking about cosine and sine, and later, tangent, as functions.

Building from the equation of a circle and the coordinates for any point on the unit circle, such as for point , leads to establishing the Pythagorean Identity, written as . Students reason about why the equation is an identity by drawing in right triangles for specific cases as they leverage the structure of the unit circle (MP7).

The notation for squaring cosine and sine is introduced in this lesson as and so students do not, for example, confuse with .