Question

Convert (-6, -6) from Cartesian coordinates to polar coordinates. Round the length to the nearest 0.01 Express the

Answer 1

9514 1404 393

Answer:

  (8.49; 225°)

Step-by-step explanation:

The angle is a 3rd-quadrant angle. The reference angle will be ...

  arctan(-6/-6) = 45°

In the 3rd quadrant, the angle is 45° +180° = 225°.

The magnitude of the vector to the point is its distance from the origin:

  √((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49

The polar coordinates can be written as (8.49; 225°).

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Additional comment

My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.