Question

Using complete sentences, define and compare radian measure to degree measure. In doing so, be sure to answer each of the following questions:
When would degree measure be appropriate?
When would radians be a better choice?
What are the pros and cons of each?
@mathmale

Answer 1

This is an example of the background knowledge we must have to do well in trig and in later courses that depend upon trig.

Measuring angles in degrees is more common in everyday life and is more likely to be familiar to people who have not studied trig in particular or math in general in great depth. Most people would recognize immediately what is meant by a "45 degree angle from the horizontal."

On the other hand, measuring angles in radians is a necessity in more advanced math applications. For example:

1) in calculating arc length, the angle MUST be in radians.
2) in formulas such as that for area of a circle (A = pi*r^2), pi (a measure of central angle) is already in radians.
3) in Calculus (which you may or may not study later on), angles are commonly expressed in radians and not in degrees.

Answer 2

This discussion may not address everything raised in this homework problem, but is a good start.

I asked you before: do you have access to a trig or pre-calculus or Algebra II textbook? If not, you might want to think about buying one of these to use as a reference (yes, seriously!).