Convert a Rectangular Equation to a Polar Equation (Multiple Examples)

Learn how to convert rectangular equations (with x and y) into polar equations (with r and θ)! This video will guide you through the essential relationships between these coordinate systems and show you how to transform equations step-by-step. We'll work through four clear examples together. In this tutorial, you will discover: Rectangular vs. Polar Coordinates: Understanding (x, y) vs. (r, θ) and their geometric representation. Key Conversion Relationships: x^2 + y^2 = r^2 (from Pythagorean Theorem) tan(θ) = y/x x = r cos(θ) y = r sin(θ) Step-by-Step Conversion Examples: Example 1: Circle (x^2 + y^2 = 121) - See how a simple substitution transforms it into polar form. Example 2: Horizontal Line (y = 7) - Learn to substitute y = r sin(θ) and solve for r. Example 3: Diagonal Line through Origin (y = √3x) - Substitute both x and y and simplify to find θ. Example 4: Vertical Line (x = 6) - Substitute x = r cos(θ) and solve for r. Simplifying Polar Equations: Using reciprocal trigonometric identities (e.g., 1/sin(θ) = csc(θ), 1/cos(θ) = sec(θ)) to write equations in their most condensed form. This video is perfect for pre-calculus and calculus students learning about coordinate system conversions. Timestamps: 0:00 - Introduction: Converting Rectangular to Polar Equations 0:30 - Understanding the Relationship Between Rectangular and Polar Coordinates 1:00 - Key Conversion Formulas (x^2+y^2=r^2, tanθ=y/x, x=rcosθ, y=rsinθ) 2:30 - Example 1: x^2 + y^2 = 121 (Converting a Circle) 3:40 - Example 2: y = 7 (Converting a Horizontal Line) 5:20 - Example 3: y = √3x (Converting a Diagonal Line through the Origin) 7:20 - Example 4: x = 6 (Converting a Vertical Line) 8:50 - Conclusion & Next Steps: Converting Polar to Rectangular Equations Don't forget to like, comment, and subscribe for more pre-calculus and calculus tutorials! #RectangularToPolar #PolarEquations #CoordinateConversion #PreCalculus #Calculus #MathTutorial #Trigonometry #Equations ➡️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