Advanced Algebra
Polar Coordinate Plane
Describe any point by a distance and an angle: plot and read polar coordinates, use negative and wrapped angles, read rays, circles and sectors on the polar grid, measure arcs, work in radians, rotate and dilate points, and move between polar and rectangular coordinates.
THE SYLLABUS
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Angle and Radius
Polar coordinates place a point by two numbers: its distance from the origin, r, and its counterclockwise angle from the positive x-axis, θ.
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Plotting in Polar
A polar point is written as the pair (r, θ): the first coordinate is the distance from the origin, the second is the angle counterclockwise from the positive x-axis.
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Identifying Points
To name a point in polar coordinates, read its circle for r and count spokes from 0° for θ; each quadrant is 90°, often split into 30° or 15° parts.
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Negative Angles
Positive angles turn counterclockwise from the positive x-axis; negative angles turn clockwise. The angle −θ points the same way as 360° − θ.
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Beyond 360°
A full turn is 360°, so adding or subtracting 360° leaves a point where it is: θ and θ + 360° name the same direction.
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Level Check
Ten questions with no hints on polar coordinates: plotting pairs, reading them off the plane, negative angles and angles past 360°.
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