This is the second of two lessons focusing on the Pythagorean Identity. The goal of this lesson is for students to deepen their understanding of the connections between , , and for an angle , using the structure of the unit circle (MP7).

First, students identify the sign of the three trigonometric values in each quadrant, which allows a reintroduction of tangent and a possible way to interpret the value of tangent as a slope. Students then consider how to use the value of cosine in Quadrant IV to calculate the values of sine and tangent at the same angle. This work prepares students for a card-matching activity in which they determine if particular values for cosine, sine, and tangent are possible or impossible in different quadrants. For possible matches, students practice using the Pythagorean Identity to calculate the two unknown trigonometric values. Throughout the matching process, students use precise language to describe the relationship between a quadrant and possible values (MP6).