Lesson Flashcards: Polar Coordinates Mathematics • 12th Grade

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The angular coordinate, 𝜃, in terms of 𝑥 and 𝑦 for 𝑥<0, 𝑦≥0

𝜃=𝑦𝑥+(180𝜋)arctanor∘

The angular coordinate, 𝜃, in terms of 𝑥 and 𝑦 for 𝑥>0

𝜃=𝑦𝑥arctan

The angular coordinate, 𝜃, in terms of 𝑥 and 𝑦 for 𝑥<0, 𝑦<0

𝜃=𝑦𝑥−(180𝜋)arctanor∘

The horizontal coordinate, 𝑥, in terms of 𝑟 and 𝜃

𝑥=𝑟𝜃cos

The angular coordinate, 𝜃, in terms of 𝑥 and 𝑦 for 𝑥=0, 𝑦<0

𝜃=−90∘ or −𝜋2

The radial coordinate

The distance, 𝑟, from the origin, where 𝑟≥0

The distance between the polar coordinates (𝑟,𝜃) and (𝑟,𝜃)

𝑑=𝑟+𝑟−2𝑟𝑟(𝜃−𝜃)cos

The angular coordinate

The angle, 𝜃, between the 𝑥-axis and the line of 𝑟, where −𝜋<𝜃≤𝜋 in radians and −180<𝜃≤180∘∘ in degrees

The angular coordinate, 𝜃, in terms of 𝑥 and 𝑦 for 𝑥=0, 𝑦>0

𝜃=90∘ or 𝜋2

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