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Find a set of polar coordinates for the point for which the rectangular coordinates are given. (3, -3 roots of 3  )?

Find a set of polar coordinates for the point for which the rectangular coordinates are given.

(3, -3 roots of 3   )

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  • 2 months ago

    Converting from rectangular to polar we have:

    (x, y) => (r, θ)

    Now, r² = 3² + (-3√3)² => 9 + 27 = 36

    Hence, r = 6

    Now, tanθ = (-3√3)/3 => -√3

    so, θ = tan⁻¹(-√3) => -60°.....i.e. 60° anticlockwise

    Therefore, θ = 300° anticlockwise

    so, (3, -3√3) => (6, 300°)

    Checking gives:

    x = 6cos300° => 3

    y = 6sin300° => -3√3

    This site is great:

    https://www.mathsisfun.com/polar-cartesian-coordin...

    :)>

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  • 2 months ago

    Rectangular coordinates (3, -3√3) to (r, θ).

    As x > 0 and y < 0, θ is in the 4th quadrant.

    r = √[3² + (-3√3)²]

    r = √(36)

    r = 6

    θ = tan⁻¹(-3√3/3)

    θ = tan⁻¹(-√3)

    θ = 360° - 60°

    θ = 300°

    Polar coordinates = (6, 300°)

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  • 2 months ago

    This is the question

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