This lecture covers the definition of tangent and cotangent functions as the quotient of sine and cosine functions, their domains, and geometric interpretations. It also explores the Pythagorean relation, values in different quadrants, axes for measuring values, and growth properties. Additionally, it discusses remarkable values, signs in different quadrants, and critical points for both functions. The lecture concludes with a summary of the key concepts learned, including definitions, interpretations, graphs, and notable values.