Question

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360 degrees

Answer 1

Pleasee help me!

Answer 2

Alright, what do you know about polar coordinates - or rather - do you know the formula for polar coordinates ?

Answer 3

No I do not

Answer 4

I can just give them to you or I could try and explain them to you, they're fairly easy to understand. Do you really want to understand polar coordinates or do you just want to be done as fast as possible ?

Answer 5

I would like to understand please :)

Answer 6

Sure thing then!

Well, up until now you've used the Cartesian system in order to define the location of a point - within this system, the position of a point in space is define through a distance on the x axis and a distance on the y axis relative to the point of origin.

Answer 7

The Cartesian system works just fine for most things that we deal with basic geometry - triangles, rectangles and so forth. The Cartesian system does suck however when it comes to circles and I'll show you why.

Answer 8

Let's say you had to describe moving from point A to point B in a straight line.

This is easily done through the Cartesian system as with the coordinates of those two points (A and B) you can easily make the function that describes the line so that if someone asks you "hey, where on Earth are you on the y axis when you're at 3 on the X axis" you can answer almost instantly.

Answer 9

But let's say that you wanted to study the movement of a point on a circle now.

Things get a little complex a bit. Instead of a line (expressed through an ax+b type of equation) we have a circle now (which has that particular nasty formula).

If we were to stay true to the Cartesian system then the coordinate of any point on that circle (let's call this point P) would be P(x,y) still - but how would you determine y if I gave you x, or x if I gave you y ? Where it was once simple to do so back when you had a line to study, now it gets a little bit more complicated due to the equation of the circle (which I wrote on the graph).

For example here, the corresponding y value of the x value of 4 would have to be taken out of the equation. Assume radius = 5 we have that

4^2+y^2=25
y^2=25-16=9
y=+/-3 (I'll explain this in a bit).

You can see how it gets a little bit more complex when it comes to circles. Hence why the polar coordinates come into play.

Answer 10

Polar coordinates are a different method of representing the position of points in space and are used solely to help you out with circles.

Instead of using two distances (one of the X axis and one on the Y axis) to represent a position, we use one distance called "radius" and one angle.

Let's take a point in space and define its position through polar coordinates.