# Homework Help: Radian Measure and the Unit Circle

1. Nov 21, 2008

### Sean Cook

I need some guidance into understanding Radian Measure and the Unit Circle. This was the topic where I tanked and had to drop the course. I'm going to pick it up again next fall and want to start preparing now.

Any help is appreciated.

Sean
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 21, 2008

### HallsofIvy

What, exactly, do you want to know? "Radian Measure and the Unit Circle" is a wide topic!

Essentially the idea of radian measure is that it IS the circumference around a unit circle cut off by an angle at the center. In particular, since a circle of radius 1 has total circumference of $2\pi$, radian measure in a circle goes from 0 to $2\pi$. A right angle cuts off 1/4 of the circle and so its measure is $2\pi/4= \pi/2$ radians. A "straight angle" cuts off 1/2 the circle and so its measure is $2\pi/2= \pi$ radians.

3. Nov 21, 2008

### Sean Cook

That makes alot more sense to me than the way is was explained, but it leads to my next trouble spot. How is a radian measured in degrees? This was where I was told to think of it like a "Clock" and that confused me and was unable to perform the calculations.

Sean

4. Nov 21, 2008

### HallsofIvy

A complete circle is $2\pi$ radians or 360 degrees. You can think of that as "$2\pi$ radians per degree" or
[tex]\frac{2\pi \text{radians}}{360 \text{degrees}}[/itex] So to go from degrees to radians you multiply by $2\pi/360$ degrees to "cancel" the degrees and get radians. That is 90 degrees is $(2\pi/360)(90)= \pi/2$ radians.

Going the other way, you just invert the fraction:
[tex]\frac{360}{2\pi}[/itex].

$\pi/3$ radians corresponds to $360/(2\pi)(\pi/3)= 360/6= 60$ degrees.

5. Nov 21, 2008

### Sean Cook

Thank you for explaining it this way, with the examples as well. I think I actually have a better understanding now :-)