Understanding Polar Coordinates Concepts

The video tutorial explains how to write four ordered pairs using polar coordinates for a given point. It contrasts polar coordinates with rectangular coordinates, where a point is represented as (r, θ) instead of (x, y). The tutorial provides examples of ordered pairs with different combinations of positive and negative values for r and θ, demonstrating how to plot points and calculate angles in standard position. It emphasizes the concept of coterminal angles and how to adjust the angle based on the sign of r and θ.

What is the main difference between polar and rectangular coordinates?

• Rectangular coordinates use angles and distances.

• Rectangular coordinates use only angles.

• Polar coordinates use only distances.

• Polar coordinates use angles and distances.

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CCSS.HSN.CN.B.4

In polar coordinates, what does a positive r value indicate?

• The point is plotted at the origin.

• The point is plotted in the opposite direction.

• The point is plotted in the same direction as the angle.

• The point is plotted on the negative x-axis.

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What is the smallest positive angle for the first ordered pair?

• 90 degrees

• 360 degrees

• 180 degrees

• 45 degrees

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CCSS.HSN.CN.B.4

For the second ordered pair, what happens when r is negative?

• The point is plotted in the opposite direction of the angle.

• The point is plotted in the same direction as the angle.

• The point is plotted at the origin.

• The point is plotted on the positive y-axis.

What is the smallest positive angle for the second ordered pair?

• 45 degrees

• 180 degrees

• 225 degrees

• 90 degrees

For the third ordered pair, what does a negative theta indicate?

• Rotation counter-clockwise from the negative x-axis.

• Rotation counter-clockwise from the positive x-axis.

• Rotation clockwise from the negative x-axis.

• Rotation clockwise from the positive x-axis.

What is one possible negative angle for the third ordered pair?

• -315 degrees

• -180 degrees

• -45 degrees

• -90 degrees

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CCSS.HSN.CN.B.4

For the fourth ordered pair, what does a negative r value indicate?

• The point is plotted on the positive y-axis.

• The point is plotted at the origin.

• The point is plotted in the opposite direction of the angle.

• The point is plotted in the same direction as the angle.

What is the greatest negative angle for the fourth ordered pair?

• -135 degrees

• -90 degrees

• -45 degrees

• -180 degrees

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CCSS.HSN.CN.B.4

In polar coordinates, what does a negative theta value indicate?

• Rotation counter-clockwise from the positive x-axis.

• Rotation clockwise from the positive x-axis.

• Rotation counter-clockwise from the negative x-axis.

• Rotation clockwise from the negative x-axis.

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CCSS.HSN.CN.B.4