1. explain the relationship between degree measures of angles, radian measure of angles, and arclength. include the following terms in your discussion
• unit circle
• circumference
• radius

i'm having a really hard time understanding this. me out.

Here's a start:

"degree measures of angles, radian measure of angles" are two mathematically related units of measurement of angles.

One full circle, measured in degrees, is represented by 360 degrees.  
One full circle, meas. in rad., is repr. by 2pi radians.

Thus, 2pi radians = 360 degrees.

If you are given an angle in degrees, you can obtain the measure of the same angle in radians by mult. the given angle by the following conversion factor:

2 pi radians

 360 degrees

Doing this will allow you to cancel out "degrees" and provide you with the equivalent angle measure in radians.