Mathematics: Determine two pairs of polar coordinates for (4,4) when 0 degrees theta 360 degrees.

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Determine two pairs of polar coordinates for

amber3687

26.01.2022

$\left(+4\sqrt{2}, 45^{\circ}\right)$ and $\left(-4\sqrt{2}, 225^{\circ}\right)$

Step-by-step explanation:

The magnitude of the polar coordinates is given by the Pythagorean Theorem:

$r = \sqrt{4^{2}+4^{2}}$

$r = \sqrt{2^{5}}$

$r = 4\sqrt{2}$

One direction of the point with respect to the origin is:

$\theta = \tan^{-1}\left(\frac{4}{4} \right)$

$\theta = 45^{\circ}$

The antiparallel version of the point is:

$r = -4\sqrt{2}$

$\theta = 225^{\circ}$

The two pairs of polar coordinates are:

$\left(+4\sqrt{2}, 45^{\circ}\right)$ and $\left(-4\sqrt{2}, 225^{\circ}\right)$

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