Lesson Flashcards: Polar Coordinates Mathematics • 12th Grade

The angular coordinate, πœƒ, in terms of π‘₯ and 𝑦 for π‘₯<0, 𝑦β‰₯0

πœƒ=𝑦π‘₯+(180πœ‹)arctanor∘

The angular coordinate, πœƒ, in terms of π‘₯ and 𝑦 for π‘₯>0

πœƒ=𝑦π‘₯arctan

The angular coordinate, πœƒ, in terms of π‘₯ and 𝑦 for π‘₯<0, 𝑦<0

πœƒ=𝑦π‘₯βˆ’(180πœ‹)arctanor∘

The horizontal coordinate, π‘₯, in terms of π‘Ÿ and πœƒ

π‘₯=π‘Ÿπœƒcos

The angular coordinate, πœƒ, in terms of π‘₯ and 𝑦 for π‘₯=0, 𝑦<0

πœƒ=βˆ’90∘ or βˆ’πœ‹2

The radial coordinate

The distance, π‘Ÿ, from the origin, where π‘Ÿβ‰₯0

The distance between the polar coordinates (π‘Ÿ,πœƒ) and (π‘Ÿ,πœƒ)

𝑑=ο„π‘Ÿ+π‘Ÿβˆ’2π‘Ÿπ‘Ÿ(πœƒβˆ’πœƒ)cos

The angular coordinate

The angle, πœƒ, between the π‘₯-axis and the line of π‘Ÿ, where βˆ’πœ‹<πœƒβ‰€πœ‹ in radians and βˆ’180<πœƒβ‰€180∘∘ in degrees

The angular coordinate, πœƒ, in terms of π‘₯ and 𝑦 for π‘₯=0, 𝑦>0

πœƒ=90∘ or πœ‹2

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