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.

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8.1 Polar Coordinates

Focus on polar conversion and polar equivalent.

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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.

01Plotting points and equivalent polar coordinatesWorked steps · five questions02Polar to rectangular coordinatesWorked steps · five questions03Rectangular to polar coordinatesWorked steps · five questions04Converting equations between formsWorked steps · five questions
Lesson brief and rules

8.1 Polar Coordinates

Convert polar (r,θ)(r,\theta ) to Cartesian using x=rcos⁡θx=r \cos \theta and y=rsin⁡θy=r \sin \theta .

Worked example 11
01 / Convert (4,0)(4,0) from polar to Cartesian.
02 / x=rcos⁡0=4,y=rsin⁡0=0x=r \cos 0=4, y=r \sin 0=0.
03 / Answer: (4,0)(4, 0)
Worked example 2 · Polar equivalent

Which polar coordinate represents the same point as (4,0)(4,0)?

A negative radius reverses direction by π\pi . Answer: (−4,π)(-4,\pi )

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.

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