Convert Rectangular Coordinates to Polar Coordinates (Formulas & Examples)

Learn how to convert rectangular coordinates (x, y) into polar coordinates (r, θ) with this complete guide! Mario's Math Tutoring breaks down the essential formulas using the Pythagorean theorem and tangent inverse. We'll go through four detailed examples, including points in different quadrants and special right triangles, highlighting crucial considerations for finding the correct angle (θ). In this video, you'll discover: 0:00 Introduction to Rectangular to Polar Coordinate Conversion 0:20 Visualizing Rectangular vs. Polar Coordinates 0:50 Formulas for Conversion: r = √(x² + y²) and θ = tan⁻¹(y/x) 1:40 Example 1: Converting (-3, 4) to Polar Coordinates 2:00 Calculating the Radius (r) 2:30 Calculating the Angle (θ) using Tangent Inverse 3:00 Important: Adjusting the Angle for the Correct Quadrant (Adding 180°) 4:00 Example 2: Converting (-5, -10) to Polar Coordinates 4:20 Calculating the Radius (r) (Simplifying Radicals) 5:10 Calculating the Angle (θ) and Adjusting for the Third Quadrant 6:20 Example 3: Converting (2, -2√3) to Polar Coordinates 6:40 Plotting the Point and Visualizing the Triangle 7:00 Calculating the Radius (r) 8:00 Calculating the Angle (θ) (Recognizing Unit Circle Values) 8:40 Multiple Ways to Represent Polar Coordinates (Negative Angles, Adding 2π) 9:30 Example 4: Converting (5√2, 5√2) to Polar Coordinates 9:50 Calculating the Radius (r) 10:40 Calculating the Angle (θ) (Recognizing Special Right Triangles) 11:00 When No Angle Adjustment is Needed Master the conversion from rectangular to polar coordinates and confidently locate points in the polar plane! #PolarCoordinates #RectangularToPolar #CoordinateConversion #Trigonometry #Precalculus #MathTutorial #MathHelp ➡️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) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join