How do you find the polar coordinates of the point?

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How do you find the polar coordinates of the point?

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Answer 1 · 2018-03-14T07:50:39

I am assuming that you want to convert a point in Cartesian Coordinate form to Polar Coordinate Form.

I will use an example in the explanation below.

Explanation:

Let us say that we want to convert a point $(0, 2)$ $(0, 2)$ in Cartesian Form to Polar Form.

Let us analyze the image below:

enter image source here

We have a right-triangle and hence we can use Pythagoras Theorem to define a relationship:

$x^{2} + y^{2} = r^{2}$ $x^2 + y^2 = r^2$

$tan θ = \frac{y}{x}$ $tan theta = y/x$

We can see that

$cos θ = \frac{x}{r}$ $cos theta = x/r$

Hence,

$x = r cos θ$ $color(blue)(x=r cos theta$ $[1]$ $color(red)([ 1 ]$

$sin θ = \frac{y}{r}$ $sin theta = y/r$

Hence,

$y = r sin θ$ $color(blue)(y = r sin theta$ $[2]$ $color(red)([ 2 ]$

Observe that, if we are given the point $(x, y)$ $(x, y)$ , then we can define $(r, θ)$ $(r, theta)$ and express $(x, y)$ $(x,y)$ in terms of $(r cos θ, r sin θ)$ $(r cos theta, r sin theta)$ .

Now, let us work on the point in Cartesian coordinate form, in our example:

$(0, 2)$ $(0,2)$

Let us plot this point and look at the graph:

enter image source here

Now, we are in a position to convert the $(0, 2)$ $(0, 2)$ to equivalent Polar form using $[1]$ $color(red)([ 1 ]$ and $[2]$ $color(red)([ 2 ]$

Polar form is $(r, θ)$ $color(green)((r, theta)$

$\Rightarrow (2, \frac{π}{2})$ $rArr color(blue)((2, pi/2)$

Hope it helps.

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How do you find the polar coordinates of the point?

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