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)(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^2x2+y2=r2

tan theta = y/xtanθ=yx

We can see that

cos theta = x/rcosθ=xr

Hence,

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

sin theta = y/rsinθ=yr

Hence,

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

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

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 color(red)([ 1 ][1] and color(red)([ 2 ][2]

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

rArr color(blue)((2, pi/2)(2,π2)

Hope it helps.