Determine two pairs of polar coordinates for the point (3, 3) with 0° ≤ θ < 360

The answer is  (3√2, 45°) and (3√2, 225°).

Step-by-step explanation:  We are given to determine two pairs of polar co-ordinates for the point (3, 3), where 0° ≤ θ < 360.

We know that the relation between Cartesian Coordinates (x,y) and Polar Coordinates (r,θ) is given by the following:

We have,

(x, y) = (3, 3).

Therefore,

and

If n = -1, then  θ = -180° + 45° = -135°,

If n = 0, then  θ = 0° + 45° = 45°,

If n = 1, then  θ = 180° + 45° = 225°,

If n = 2, then  θ = 360° + 45° = 405°, etc.

Since  0° ≤ θ < 360, therefore the value of  θ is 45° and 225°.

Thus, the two pairs of polar co-ordinates are (3√2, 45°) and (3√2, 225°).

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step-by-step explanation:

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