Convert from Polar Coordinates to Rectangular Coordinates (Formulas & Examples) скачать в хорошем качестве

Convert from Polar Coordinates to Rectangular Coordinates (Formulas & Examples)

Learn how to convert polar coordinates (R, θ) to rectangular coordinates (X, Y) with this comprehensive tutorial! This video will show you the key formulas and walk you through four detailed examples, including cases with positive/negative radii and angles in both radians and degrees. In this tutorial, you will discover: Understanding Polar vs. Rectangular Coordinates: Visualizing how points are located in both systems. The Conversion Formulas: Deriving X = R cos θ and Y = R sin θ using a right triangle and trigonometry. Step-by-Step Conversion Process: Identifying R (radius) and θ (angle) from the polar coordinates. Plugging R and θ into the conversion formulas. Evaluating cosine and sine of the angle (using the unit circle or a calculator). Calculating X and Y values. Writing the final answer in (X, Y) rectangular form. Working with Different Angles: Angles in radians (e.g., 2π/3, 5π/6, -3π/4). Angles in degrees (e.g., 215°). Handling Negative Radii: How a negative R value affects the location of the point and the final X and Y coordinates. Unit Circle Review: Quick refreshers on cosine and sine values for common angles. Calculator Usage: When to use a calculator for angles not on the unit circle, and ensuring your calculator is in the correct mode (degrees/radians). Visualizing the Conversion: Confirming that the converted (X, Y) point corresponds to the original (R, θ) location on the graph. This video is perfect for pre-calculus and trigonometry students learning about coordinate systems and conversions! Timestamps: 0:00 - Introduction to Polar to Rectangular Coordinates 0:25 - Visualizing Polar vs. Rectangular Coordinates 1:00 - Deriving the Conversion Formulas: X = R cos θ, Y = R sin θ 2:30 - Example 1: Convert (4, 2π/3) to Rectangular 3:00 - Using the Unit Circle for cos(2π/3) and sin(2π/3) 4:00 - Calculating X and Y 4:30 - Example 2: Convert (-2, 5π/6) to Rectangular 5:00 - Locating Points with Negative Radii 5:40 - Using the Unit Circle for cos(5π/6) and sin(5π/6) 6:50 - Calculating X and Y 7:20 - Example 3: Convert (3, 215°) to Rectangular (Using Calculator) 8:00 - Ensuring Calculator is in Degree Mode 8:50 - Example 4: Convert (-5, -3π/4) to Rectangular 9:20 - Locating Points with Negative Angles 10:10 - Using the Unit Circle for cos(-3π/4) and sin(-3π/4) 11:40 - Calculating X and Y 12:10 - Conclusion & Next Steps (Converting Equations) Don't forget to like, comment, and subscribe for more pre-calculus and trigonometry tutorials! #PolarToRectangular #CoordinateConversion #PreCalculus #Trigonometry #UnitCircle #MathTutorial #RectangularCoordinates #PolarCoordinates ➡️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)    / @mariosmathtutoring