How do you write the polar coordinates for the point with rectangular coordinates (0, 3)?

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How do you write the polar coordinates for the point with rectangular coordinates (0, 3)?

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Answer 1 · 2015-11-06T04:28:03

$(3, 90^{\circ})$ $(3,90^\circ)$

Explanation:

Polar coordinates are in the form $(r, θ)$ $(r,theta)$

First we need to find the vector, it goes from the origin $(0, 0)$ $(0,0)$ to your point $(0, 3)$ $(0,3)$ .

$\to u = < 0 ˆ i + 3 ˆ j > - < 0 ˆ i + 0 ˆ j > = 0 ˆ i + 3 ˆ j = 3 ˆ j$ $\vec{u}=<0\hat{i}+3\hat{j}> - <0\hat{i}+0\hat{j}> = 0\hat{i} + 3\hat{j}=3\hat{j}$

You can see the vector goes straight up, just in the $y$ $y$ direction, so the angle is $90^{\circ}$ $90^\circ$ and the radius $r$ $r$ is 3. Let's prove that.

As we said, your vector $\to u = 3 ˆ j$ $\vec{u}=3\hat{j}$ . Let's find the modulus (radius) of the vector:

$r = ∣ ∣ \to u ∣ ∣ = \sqrt{3^{2}} = 3$ $r=|\vec{u}|=\sqrt{3^2}=3$

And the angle will be:

$θ = arctan (\frac{3}{0}) = 90^{\circ}$ $theta =arctan(3/0)=90^\circ$

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How do you write the polar coordinates for the point with rectangular coordinates (0, 3)?

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