MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

MathLabwith Mr. Ahmed
Free preview

8.2 Graphs of Polar Equations

Focus on constant polar radius and polar line.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Graphing basic polar equationsWorked steps · five questions02Symmetry testsWorked steps · five questions03Cardioids, limaçons, roses and lemniscatesWorked steps · five questions
Lesson brief and rules

8.2 Graphs of Polar Equations

For r=r= constant, the polar graph is a circle centered at the pole.

Worked example 11
01 / For r=4r=4, find the distance of any point on the graph from the pole.
02 / A constant positive radius r=4r=4 describes a circle of radius 44.
03 / Answer: 44
Worked example 2 · Polar line

What graph does θ=π2\theta =\dfrac{\pi }{2} represent?

All points have direction π2\dfrac{\pi }{2} or the opposite via negative rr. Answer: Vertical line through pole

Read the graphs

Graphing basic polar equations

Describe the graph of r=6cos⁡θr = 6 \cos \theta .
Graph for Graphing basic polar equationsThe graph corresponds to the stated function or supplied points.−22468−4−3−2−11234xy
Solid: curve 1 · Dashed: curve 2

Answer: Circle, center (3,0)(3, 0), radius 33

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

Read this lesson preview