Converting (-2, 2√3) to Polar

Trigonometry · Axiom Academy

EXAMPLE Converting Rectangular to Polar Coordinates Learn to convert from (x, y) to (r, θ) format by finding the radius and angle step-by-step. Excellent work! You've successfully converted rectangular coordinates to polar form. Here's what we learned: Radius Formula: Use r = √(x² + y²) to find the distance from the origin. This value is always positive. Quadrant Matters: The signs of x and y determine the quadrant, which affects the angle calculation. Don't just use arctan directly! Reference Angles: Find the reference angle first using |y/x|, then adjust based on the quadrant. Quadrant II Adjustment: When x 0 (Quadrant II), use θ = π - reference angle. Verify Your Answer: The angle should make sense based on the location of the point in the coordinate plane. This conversion process is essential for working with polar equations and understanding how rectangular and polar coordinate systems relate. Practice with points in all four quadrants to build confidence!

This is the written version of the interactive lesson above. See the full Trigonometry course.