-515 is no the simplest form for this angle.
See, 900 degrees is the same angle as 180 degrees, and one of the ways I like to check that that's true -- if I have a calculator handy --is to plug in sin(180) and sin(900), and if they are the same angle, they'll give me the same answer. And they do, 0 for both of them.
Let's try and find the simplified angle for -515. Now, that negative might look scary, but it just means that the angle was found by going clockwise, unlike the normal way where we move counter-clockwise.
So we'll ignore the negative sign for now. The first thing I do is imagine drawing a line all the way around the circle
That used up 360 degrees. Now we have 115 degrees left
Now I move another 90 degrees
Now I have 65 degrees left
Now we can look at the final picture and see how many degrees it would take to reach this angle, but going in a clockwise direction . That'll give us our reference angle
So, we'll need to go 180 degrees. And we know that we used up 65 degrees, so there are 25 degrees left in that qudarant. 180 + 25 gives us 205
So, we are saying that 205 and -515 are two different ways to reference the same angle. Let;s plug them into sin(theta) and find out!
sin(205) = -0.4226
sin(-515) = -0.4226
Yep! The reference angle for -515 is 205
