1. Radians & Arc Lengths
Section 5.2

2. Definitions
If you were to take the radius of a circle and wrap it on the circumference, the angle you create is called one radian.
1 rad

3. Degrees and Radians
How many radians do we have in a circle? Think about the circumference… C = 2π × radius So… there are exactly 2π radians on a circle! How many radians on a half of circle? π
Each radius forms 1 RAD!

4. 360˚ = 2π rad 180˚ = π rad 90˚ = π/2 rad (90˚ is ¼ of a circle)
Degrees and Radians
360˚ = 2π rad 180˚ = π rad 90˚ = π/2 rad (90˚ is ¼ of a circle)

5. Converting from Degrees to Radians
We can convert from one to the other using the following ratio: degrees = radians 180 Π ***NOTE 1 turn = 360˚

6. Example 1
Convert the following: 3 rad x = π x = 540˚ or 171.9˚ π

7. Example 2
Convert the following: 120˚ 120 = x 180 π x = 2π rad or 2.09 rad 3

8. Arc Length
The length of an arc on the circle that is marked off by the rays of a particular angle (measured in radians!) s = rӨ s r Ө r

9. Example 3
Find the arc length if we know: r = 2cm and Ө = π/3 rad s = rӨ s = 2(π/3) s = 2.09cm

10. HOMEWORK
Workbook p #1-6 p.196 #7, 8, 9