How do you find the polar coordinates of the point?

1 Answer
Mar 14, 2018

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) 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

tan theta = y/x

We can see that

cos theta = x/r

Hence,

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

sin theta = y/r

Hence,

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

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

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

(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) to equivalent Polar form using color(red)([ 1 ] and color(red)([ 2 ]

**Polar form is ** color(green)((r, theta)

rArr color(blue)((2, pi/2)

Hope it helps.