1. What is a RADIAN?!?!

2. ♪♪Twinkle Twinkle Little Star Circumference Equals 2πr♪♪
Length of an arc (Arc Length): s = rθ
s = (πrθ)/180
1 Revolution (Circumference):
s = 2πr
A radian is a unit of an angle equal to the angle at the center of a circle whose arc is equal to the length of the radius.
How many degrees is a radian??

3. Arc Length Example
A circle/pizza/tire/any round object has a radius of 6 inches. Find the length of the arc intercepted by a central angle of 120∘.

4. Area of a Sector Example
For a circle of radius 𝑟, the area 𝐴 of a sector with central angle 𝜃 is given by
𝐴 = (1/2)r2𝜃
where 𝜃 is measured in radians.
Example
A sprinkler sprays water over a distance of 30 ft while rotating through an angle of 150∘. What area of lawn receives water?

5. Converting Radians  Degrees
To convert from radians to degrees, multiply the number of radians by 180°/π radians.

6. Examples
Convert radians to degrees.
Convert radians to degrees.

7. Converting Degrees  Radians
To convert from degrees to radians, multiply the number of degrees by π radians/180°.

8. Examples
Convert 90° to radians.
Convert 120° to radians.