Explore polar equations and their applications in calculus through this comprehensive 1.5-hour tutorial. Dive into converting between Cartesian and polar coordinates, calculate slopes of tangent lines to polar curves, and master the techniques for finding dy/dx. Learn to determine the area enclosed by polar curves and regions, and understand the proof for arc length of polar curves. Tackle a variety of problems, including specific examples like the polar curve r = tan(theta) at pi/3 and r = 1/theta at pi, to solidify your understanding of these advanced mathematical concepts.