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This lecture covers trigonometric, logarithmic, and exponential functions, focusing on the rotation of a vector in a plane. Starting with defining a coordinate system in the plane, it explains how to determine the components of a vector and how to rotate it around the origin. The lecture presents a method to find the components of the rotated vector and introduces the concepts of sine and cosine functions to calculate them. It concludes with a proposition on rotating a vector around the origin and expressing the rotated vector in matrix form.