Polar Coordinates: Converting Between Rectangular and Polar Forms

In this lesson, we explore polar coordinates and how they connect to the rectangular coordinate system. Students learn how to convert between rectangular (x,y) and polar (r,θ) forms using key relationships derived from geometry and trigonometry. Starting with SOHCAHTOA, we show how: cos(θ) = x / r → x = r cos(θ) sin(θ) = y / r → y = r sin(θ) tan(θ) = y / x We also connect these to the Pythagorean Theorem: x² + y² = r² With these four foundational relationships, students are able to move fluidly between rectangular and polar coordinates and understand how both systems describe the same points in different ways.