1. Terms to know going forward
Angle: 2 rays an initial side and a terminal side.
Terminal side
Initial side
Positive angle goes counter clockwise. Negative angle goes clockwise.
Standard position: vertex of angle at origin
Quadrants: II I
Where is x positive and negative III IV
Where is y positive and negative
Degrees: a rotation from the initial side all the way around to itself ( 1 revolution) is 3600 , 10 = 1/360 of a revolution.
900 = ¼ of a revolution
1800 = ½ of a revolution.

2. Radians: 1 radian is when the initial ray and terminal ray of an angle are the same length as is the arc of the circle the intersect. This is helpful to understand how to convert from degrees to angle and vice versa.
Using this definition and the fact that the circumference of a circle is 2πr if the radius is 1 then the number of radians to make 1 revolution can be found by setting rø = 2πr (circumference) solve for ø and you get ø = 2π or one revoulution is equal to 2π
Therefore 3600 = 2π radians
Dividing both side by 2 you find that 1800 = π radians
Dividing both sides by 180 you find that 10 = π/180 radians or
Dividing both sides by π you find that 1800/π = 1 radian.
We can use these 2 formulas to convert from degrees to radians and vice versa.

3. Degrees and Radians of a Circle
There are 3600 in a circle and if the circle has a radius of 1 then there are 2π radians around the circle. Therefore we can measure a circle in degrees or radians.
How can you convert degrees to radians?
So change 1000 to radians

4. Degrees and Radians of a Circle
So change 180 to radians
You Try
So change 3150 to radians to radians

5. Degrees and Radians of a Circle
There are 3600 in a circle and if the circle has a radius of 1 then there are 2π radians around the circle. Therefore we can measure a circle in degrees or radians.
How can you convert radians to degrees?
So change π/4 to degrees

6. Degrees and Radians of a Circle
So change 5π/3 to degrees
You Try
So change 11π/12 to degrees π/2 to degrees

7. 900 or
-2700 00
or 3600
2700
-900
1800
-1800
What does some of this look like on a circle.
Degrees

8. Radians π/2 or -3π/2 Or 2π 3π/2 -π/2 π -πOr 2π
3π/2
-π/2 π -π
What does some of this look like on a circle.
Radians

9. Formulas: must use radians
Arc of a sector Area of a sector
s = rø A = ½ r2 ø
If the radius is 3 and the angle is 450 find the arc and area.
450 = π/4
s = 3(π/4) = A = ½ (3)2(π/4) =3.534