How do you find the reference angle for -515 degrees?

`-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

![https://www.wolframalpha.com/input/?i=reference+angle+for+360+degrees]()

That used up `360` degrees. Now we have `115` degrees left

Now I move another `90` degrees

![https://www.wolframalpha.com/input/?i=reference+angle+for+-450+degrees]()

Now I have `65` degrees left

![https://www.wolframalpha.com/input/?i=reference+angle+for+-515+degrees]()

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`