Polar Review 3-4

Front

What is the polar coordinate system?

Back

A two-dimensional coordinate system where each point is determined by a distance from a reference point (origin) and an angle from a reference direction.

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CCSS.HSN.CN.B.4

Front

What is the relationship between polar and rectangular coordinates?

Back

Polar coordinates (r, θ) can be converted to rectangular coordinates (x, y) using the formulas: x = r * cos(θ) and y = r * sin(θ).

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CCSS.HSN.CN.B.4

Front

How do you convert rectangular coordinates to polar coordinates?

Back

To convert (x, y) to polar coordinates (r, θ): r = √(x² + y²) and θ = arctan(y/x).

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CCSS.HSN.CN.B.4

Front

What is the formula for converting polar coordinates to rectangular coordinates?

Back

To convert (r, θ) to rectangular coordinates (x, y): x = r * cos(θ) and y = r * sin(θ).

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CCSS.HSN.CN.B.4

Front

What does the variable 'r' represent in polar coordinates?

Back

The distance from the origin to the point.

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CCSS.HSN.CN.B.4

Front

What does the variable 'θ' represent in polar coordinates?

Back

The angle measured from the positive x-axis to the line connecting the origin to the point.

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CCSS.HSN.CN.B.4

Front

How do you find the angle θ in polar coordinates when given rectangular coordinates?

Back

Use θ = arctan(y/x), adjusting for the quadrant of the point.

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CCSS.HSN.CN.B.4

Front

What is the polar coordinate for the point (0, 0) in rectangular coordinates?

Back

(0, θ) for any angle θ, since the distance from the origin is zero.

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CCSS.HSN.CN.B.4

Front

What is the significance of the angle being measured in radians or degrees in polar coordinates?

Back

It determines the direction of the point in relation to the positive x-axis.

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CCSS.HSN.CN.B.4

Front

How do you convert the polar coordinate (5, 50°) to rectangular coordinates?

Back

x = 5 * cos(50°), y = 5 * sin(50°) which results in approximately (3.2, 3.8).

Tags

CCSS.HSN.CN.B.4