Converting Rectangular Coordinates to Polar

This is another quick and easy one. If it seems like I'm beating the easy ones to death it's because we're going to hate ourselves if we forget these because we're rusty and lose points on them. I may add a video lesson at a later time, but for now, here's a quick and dirty guide to converting rectangular coordinates to polar.

Before we begin, be aware of what we're talking about. Rectangular coordinates are the common form of a coordinate. On the plane, these are our everyday "x-y" coordinates, which take the form of (X, Y). We're all familiar with these.

To refresh your mind if you've forgotten what polar coordinates are, they are simply coordinates expressed as a radius and an angle. They take the form of (r, Θ). That's "theta" for those of you who don't see it in computer-font often. 


There are two equations to know. They're on page 23 of your Supplied Reference Manual. The most important thing to do on these easy plug-and-chug questions is to get familiar with the manual so if you forget the formula, at least you have a hunch about where to find it.

r = sqrt(x^2 + y^2)

Θ = tan^-1(y/x)

Easy. So let's try an example. 

EXAMPLE: Convert the rectangular coordinates (2, 3) to polar coordinates.

TIP: Remember the order of operations. If you're given a negative rectangular coordinate, for example the -3 in (9, -3), you're not taking the square root of 9^2 - 3^2. It's 9^2 + (-3)^2. This is important because when you square that negative value, the negative sign drops, so you'll be doing a completely different operation if you get the order of operations mixed up.

TIP: Be aware of whether your calculator is in degrees or radians. This will affect your answer for theta and they might try to trick you on this one.
 
PRACTICE PROBLEMS: Convert the following rectangular coordinates to polar coordinates.

a) (1, 9)
b) (2, -2)

You can write your own practice problems if you need more. Write a big long sheet of as many as you think you need and work them. Then go to WolframAlpha and punch them in. Scroll down to the bottom and it will translate them to polar coordinates.

ANSWERS:
Hilight the text with your mouse to reveal the solutions.

Problem a) (9.05, 6.34°)
Problem b) (2.83, -45°)