Radians & Arc Lengths Section 5.2

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

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!

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)

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˚

Example 1 Convert the following: 3 rad x = 3 180 π x = 540˚ or 171.9˚ π

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

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

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

HOMEWORK Workbook p.194-195 #1-6 p.196 #7, 8, 9