Simplifying an Angle

So, if I have an angle, say it's 135o, that simplified would be 45o right? But if I have an angle, say 330o, it simplifies to 30o rather than 60o? Why?

Here is a page with some pretty and interactive diagrams (if you scroll down a bit) that may help you.

https://www.mathsisfun.com/algebra/trigonometry.html

Take a look at what happens if you put the angle at 135 degrees and at 330 degrees.  You will see the acute angle ath must be used.

Let me know how you get on.

because it can simplify farther than that

plus it doesn't go in evenly

When dealing with sin, cos, and tan, there are results for a 60^o angle. The cos of 60^o is 1/2, the cos of 30^o is sqr root (3)/2. If I have 12(cos 330^o + i * sin 330^o) I need to know why I simplify that to 30^o.

Okay... so, if the angle forms an acute triangle, the angle is what still must be gained to reach 360^o. For example, it is 30^o more to 360^o in this acute angle, so the angle is 30^o. However, if the angle is a right angle, then it simplifies to how much it is past the last checkpoint, for example, 135^o is 45^o more than 90^o therefore, the resulting angle is 45^o. I am not good with math terms, but I think I get it.

Okay, I found out how to do it, wow. That moment when you figure out that the way that you have been doing things, is all a lie. Thank you so much for your help. I'm gonna facepalm for a while and blame Saxon math lol.