FLASHCARD for MAJOR GRADE - Polar Coordinates and Equations

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What are Polar Coordinates?

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Polar coordinates are a two-dimensional coordinate system where each point is determined by a distance from a reference point (the pole) and an angle from a reference direction (the polar axis).

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CCSS.HSN.CN.B.4

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How do you convert Cartesian coordinates (x, y) to Polar coordinates (r, θ)?

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To convert from Cartesian to Polar coordinates, use the formulas: r = √(x² + y²) and θ = arctan(y/x).

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CCSS.HSN.CN.B.4

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What is the formula for converting Polar coordinates (r, θ) to Cartesian coordinates (x, y)?

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To convert from Polar to Cartesian coordinates, use the formulas: x = r * cos(θ) and y = r * sin(θ).

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CCSS.HSN.CN.B.4

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What is the significance of the angle θ in Polar coordinates?

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The angle θ represents the direction of the point from the origin, measured counterclockwise from the positive x-axis.

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CCSS.HSN.CN.B.4

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What does the radius r represent in Polar coordinates?

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The radius r represents the distance from the origin to the point in the Polar coordinate system.

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CCSS.HSN.CN.B.4

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How do you find the distance between two points in Polar coordinates?

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To find the distance between two points (r1, θ1) and (r2, θ2), use the formula: d = √(r1² + r2² - 2*r1*r2*cos(θ2 - θ1)).

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CCSS.HSN.CN.B.4

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What is the Polar equation of a circle centered at the origin?

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The Polar equation of a circle centered at the origin with radius a is given by: r = a.

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CCSS.HSN.CN.B.4

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How do you graph Polar equations?

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To graph Polar equations, plot points for various values of θ, calculate the corresponding r, and then plot these points in the Polar coordinate system.

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CCSS.HSN.CN.B.4

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What is the Polar equation of a line through the origin?

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The Polar equation of a line through the origin making an angle θ with the positive x-axis is given by: θ = constant.

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CCSS.HSN.CN.B.4

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What is the Polar equation of a spiral?

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The Polar equation of a spiral can be expressed as r = aθ, where a is a constant.

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CCSS.HSN.CN.B.4