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This lecture covers the properties and limits of trigonometric functions, focusing on cosine and sine functions. It explains how to determine the limits of these functions as x approaches 0 or 1, emphasizing their even nature. The lecture also discusses the relationships between cosine, sine, and tangent functions, highlighting the importance of understanding these relationships for evaluating limits. Additionally, it explores the concept of function parity and provides examples to illustrate the calculations involved in determining limits for trigonometric functions.