Polar Function Graphs
Polar graphs are swept, not plotted: θ turns while r = f(θ) sets the distance from the pole. Three families cover the course. Circles: r = a is centered at the pole, but r = a cos θ passes THROUGH the pole with center (a/2, 0) and diameter a. Roses: r = a sin(nθ) grows n petals for odd n and 2n petals for even n, each of length a. Limaçons: comparing a to b in r = a ± b sin θ predicts an inner loop (a < b), a cardioid (a = b), or a poleless curve (a > b).
The mistakes are tracing mistakes: handing in the rectangular r-versus-θ wave as the polar picture, centering every circle at the origin with radius a, miscounting petals by ignoring the parity rule, and treating negative r as undefined instead of folded across the pole. All four are drilled in the lesson.
The work
3 ways in · any order
Lesson
Polar Function Graphs
›
Sweep, do not plot. The lesson reads circles, roses, and limaçons straight from their equations, derives the odd-n and even-n petal counts from the negative-r fold, and locates every pole crossing. Ten scenarios close it out: identify, count, and trace without a picture.
Diagnostic
10-item topic check
›
Ten items on the Topic 3.14 tracing errors: wave-as-picture reads, misplaced circle centers, petal miscounts, and negative-r mishandling. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.