There are two ways of measuring angles - not with a protractor and compass silly! I'm talking about Degrees and Radians. You know what degrees are (angle degrees, not temperature) but what are radians? Look at it this way: degrees is the real world, practical method while radians is the mathematical, theoretical method. Fortunately for us, your calculator knows both and can convert between the two!
We'll start with what you already know - degrees. When we're looking at angles, imagine the angle simply as a wedge out of a circle (or a slice of pie). Why should you worry about a whole circle? Because that's what we base the standard on! There are 360° in a circle. That funny little ° is the notation for 'degree' - kinda like in for 'inches' and lbs for 'pounds'. So we're really just comparing the angle to a full circle. A half circle has half the degrees - 180°. A quarter circle - 90°, and so on.
Another handy trick: if you know an angle as a fraction of a circle, you can find the angle in degrees real easily. Say you have a pie sliced into 6 equal pieces, what's the angle of one piece? That's not hard.
The most common usage of degree measurements is a globe or a map. Those longitudes and latitudes are actually degree marks. But wait! What are those funny marks after the degree sign? Well the world is a big place and to make things easier to find, the space between each degree is split into minutes (') which are are further split into seconds (") - you know, like on clocks, remember that all the first clocks were round. This real world method of measuring things in degrees, minutes, seconds is usually abbreviated to DMS.
It may sound confusing at first, but it makes things so much easier. Wouldn't it be easier to find 45°38'29" on the map compared to 45.6413887°? Thought so. How'd I get that number? Well, there 60' in 1° and likewise 60" in 1' - just like a clock! That mean's 30' is ½ a degree - useful to know if you're estimating.
Now that you understand how to measure angles - here's another twist: mathematicians don't use degrees, they measure in radians.
note: the concept of radians is fairly difficult and doesn't appear in math classes until pre-calculus. If you haven't made it this far yet, and you're not a masochist or a eager-beaver, you may want to skip this section and go straight to the calculator part.
Radians aren't too much different from degrees - they're just a different way of measuring angle, sort of like yards are different from meters. The unit for radians is also based on a complete circle (360°) which happens to be 2pi. I don't mean grandma's pie, I mean the mathematical pi (3.14159..) that i don't have a niffty key to type in so you can see it. We include it when writing radian numbers because it is a magic little number that makes it all work out. Does anything look familiar? Maybe the equation for the circumference of a circle rings a bell: 2piR. That's right, you can find the circumference of a circle (or wedge) by multiplying the angle (in radians) by the radius - I wonder where they got that name?
Also like degrees, we can find the angle of our wedge if we know its proportion to a circle. Here's the bigges:
You probably noticed that they're all written as fractions. Radians are almost always written as fraction because if your using radians, you're probably working with trig and that means everyone's favorite 30/60, right triangles! I also wrote the degree conversion for each radian because (at least for me) it's easier to think of degrees in your head than remember radians.
Also unlike degrees, there is no smaller unit like ' and " for radians, just smaller fractions. One import thing to remember when working with radians to always remember your 'pi'. There's a big difference between ½ and ½ * 3/14159.. Using it in radian notation also makes it easier to remember, ½pi is so much easier than 1.570796 radians, don't you think?
Did you catch all that? That's all right, your math monkey already knows all that. It's a master at degrees and radians and how to convert the two.
First off, you need to make sure you're in the correct setting (duh, if you're working in degrees - the calculator needs to be set to degrees!) From the [MODE] window, you can toggle between Radian and Degrees on the 3rd line. note: Radian is the default
When you're in degree mode, anything that calls for an angle will assume the number you give it is in degrees (and likewise for radian mode, just have to remember to include pi). Of course, there's some niffty things for working with angles in (you guessed it) the Angles menu.
The first two items, the degree symbol and the minute symbol, are for when you're writing in dms notation. Where's the second symbol you ask? That's easy, you can find the " on the keyboard above the + sign, [ALPHA] ". The third symbol 'r' is to signify that the number is in radians. The fourth entry, >dms, will convert any decimal degree into dms notation. The last four entries are unimportant for you. They are used to convert standard xy coordinates into polar coordinates and visa versa. Confused? That's because this isn't something needed in High School math and it's probably best just to ignore these strange entries.
But wait! That's not all, say you have an angle in radians and you want it in degrees. Since your answer will be in degrees, be sure to set your mode to degrees. Then, simply put in your radian angle with the 'r' symbol on the end. Hit ENTER and watch monkey magic! And voila, a degree!