Hello spigoteers! It just shot to my mind that I never actually explained what radians are. To me, that is quite a panic situation, because that means you've been using Math#toRadians() without knowing what it is for. So here I am today, to explain what radians are. So, this is the unit circle. As you can see it's divided in some degrees. I hope you know what degrees are. If you don't I honestly don't know what you're doing here. The full circle is 360 degrees. The perimeter of this circle is 2π, because the radius is 1, and the formula to calculate the perimeter is 2rπ, and since the radius is 1, it becomes 2 * 1 * π, which is equal to 2π. Keep that in mind. Now, this is Fredrik. Fredrik likes to walk. He decides to walk on the outside of the unit circle. He walks a whole circle, which means he returned back to where he started. But, what's the distance Fredrik has walked? It's 2π, because the perimeter of the unit circle is 2π. This is what radians are. 360 degrees belong to 2π. It's how far you are on the circle at a certain degree. So what radians goes with 180 degrees? 2π is the full circle, so it's π. But then what goes with 90 degrees? 90 is 1/4 of 360, is it's 2π / 4, which is π/2. We can add some radians values to the unit circle. This is the result: This is basicly what radians are! It's not that hard. But, you might think, why not just use degrees? In some cases, radians are better and easier to use and you will love them. As for Java, you gotta use them because the sin and cos functions work with radians. Now this does not mean radians stop at 2π or start at 0. You can also have a radians value of -π or 3π. Funny thing is that -π and 3π are both at the same location on the circle. Because 2π is a full circle, you can substract that from 3π, and what you have left is 1π = π then, which is at 180 degrees. -π simply is the same as π but in the opposite direction. Remember Fredrik? He simply started walking in the other direction. Now do not fear, there are 2 very simple formulas to turn a degree into a radians and the other way around. degrees = radians * 180 / π radians = degrees * π / 180 The second formula is basicly what Math#toRadians(double) does. I hope it's now clear to you what radians are! If you have any questions feel free to leave a comment down below. Thanks for reading! - Finn

I don't understand... Spoiler Why can't I be as good at explaining basic concepts as you? I tried (and failed) to teach someone concavity today

My mother is a high-school english teacher (Yes she works at my school), she has thaught me quite a few things about teaching. I've also given math classes to high-school classes, my teacher also taught me some stuff about teaching. I didn't start out of nowhere Grades are different all around the world. There are a lot of people at my school who have no idea what radians are (I don't blame them, you don't need this in life), I'm 16 and I'm turning 17 this school year.

Depends on who is reading this. Honestly, I know people taking calculus this year who still haven't learned radians and are going into a class where you kinda need to know what they are.

Take it back. Seriously though, think about some practical uses of radians. Polars. Say you have a solar system and you're trying to model the position of planets rotating around a point. Impossible with a cartesian function but trivial (r=x) in a polar function. Edit: Don't worry, the further you go in Calculus the more practical it becomes.

Why didn't you use tau? It makes understanding radians so much simpler. τ is a whole turn around the unit circle, τ/2 is half a turn. τ/4 is a quarter etc

That's very kind of you sir! You might wanna change that And great tutorial, I didn't know what radians where before and thanks to your tutorial I will now be able to sleep in one of my upcoming math courses! Cheers

I believe I'm not familier with tau. This is how it was explained to me and it all became clear to me quite fast, so I decided to explain it like this as well. If you have a few links to some more information about 'tau' I could possibly add it to the original post.

Because we don't need it. Honestly, it's like saying, hey we have this wonderful thing called the kilogram! It measures mass! Now we also have these other 10 non-base units that do the same thing!

Tau is basically a superior mathematical constant defined as 2*pi (It's also the ratio of a circle's radius to its circumference) You can look up Vi Hart on Pi for many rants on why pi is bad and tau is good. There's also this site http://tauday.com/

Ok, I will look some stuff up. Just to everyone, let's not start a discussion on which one to use, I'll read up about it and decide which one I prefer (so also the one to be put in the tutorial).