Master graphing limaçons (pronounced "lee-ma-sons") in this comprehensive tutorial from Mario's Math Tutoring! Derived from the French word for "snail," these fascinating polar curves are a key topic in pre-calculus and trigonometry. This video will guide you through all four types of limaçons with detailed examples and a unique method for graphing. Learn to identify and sketch: Limaçons with an Inner Loop Cardioids (A/B = 1) - the heart-shaped curve! Dimpled Limaçons Convex Limaçons We'll use a powerful technique of first graphing in the Cartesian plane (XY plane) to easily transfer points to your polar graph. Understand how the ratio of A/B determines the shape and how symmetry (cosine vs. sine) helps in plotting. Plus, get extra practice problems to solidify your understanding! Timestamps: 0:00 Introduction to Graphing Limaçons 0:20 What is a Limaçon? (French for Snail) 0:40 Identifying Limaçon Equation Form (R = a ± b cos/sin θ) 0:55 How to Determine Limaçon Type (A/B Ratio) 1:05 Inner Loop 1:15 Cardioid (A/B = 1) 1:25 Dimpled 1:35 Convex 1:55 Example 1: Graphing R = 1 + 2 cos θ (Inner Loop) 3:55 Understanding Negative R-values in Polar Graphs 5:30 Example 2: Graphing R = 3 - 3 sin θ (Cardioid) 7:50 Cartesian Plane Method for Polar Graphs 9:45 Example 3: Graphing R = 3 - 2 cos θ (Dimpled) 13:00 Example 4: Graphing R = 6 + 2 sin θ (Convex) 15:00 Practice Problem 5: R = 2 - 2 cos θ (Cardioid) 18:00 Practice Problem 6: R = 4 - cos θ (Convex) 20:50 Practice Problem 7: R = 1 - 3 sin θ (Inner Loop) 25:00 Practice Problem 8: R = 4 + 3 sin θ (Dimpled) ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)