First of all, arccos = .4567 is 62.8 degrees (punch it in your calculator to find out).

It's in quadrant one, therefore you don't need a reference triangle because well, I don't know how to explain it. You just don't.

Say you wanted to find arc cos= a value that gets the angle into quadrant 2.

I cannot explain how come, as my knowledge is little. Check youtube or google. The goal is to get the angle into something the 1st quadrant can handle (90 degrees or under). How come? I don't know.

What you do is do 180 degrees-the angle and that's it. (works also for radians as pi= 180 degrees

For the 3rd quadrant,

angle - 180 degrees

4th,

360 - angle

Say from some trig function with a decimal, you get angle 340 degrees.

Now, we know that's in the 4th quadrant as each quadrant (section of the graphing plane) contains the degrees 270 (could be 271) to 360.

So we use, 360 - 340= 20.

Hope that helps some.