Name:_____________________________
Date:________________________
Radian Measure
An angle is determined by rotating a ray (half-line) about its endpoint. The starting position of
the ray is the initial side of the angle, and the position after rotation is the terminal side.
How are positive and negative angles generated?
The measure of an angle is determined by the amount of rotation from the initial side to the
terminal side. One way to measure angles is in radians.
𝑠
One Radian: θ = 𝑟 θ = Central Angle s = Arc Length r = Radius
θ is measured in radians
Degree Measure
𝜋
360° = 2π rad and 180 = π rad. Meaning 1° = 180
Converting between Degrees and Radians
𝜋 𝑟𝑎𝑑
1. To convert degrees to radians, multiply degrees by 180
2. To convert radians to degrees, multiply radians by
180
𝜋 𝑟𝑎𝑑
Example 1: Converting from Degrees to Radians
a. 135°
b. 540°
c. -270°
d. 40°
c. 2 rad
d.
Example 2: Converting from Radians to Degrees
𝜋
a. - 2 rad
b.
9𝜋
2
rad
3𝜋
4
rad
Arc Length: s = r * θ
Example 3: A circle has a radius of 4 inches. Find the length of the arc intercepted by a
central angle of 240°.
Example 4: A circle has a radius of 1.4 feet. Find the length of the arc intercepted by a central
angle of 330°.
Name:_____________________________
Date:________________________
Area of a Sector: A = ½*r2*θ
Example 5: A sprinkler on a golf course fairway is set to spray water over a distance of
70 feet and rotates through an angle of 120°. Find the area of the fairway watered by the
sprinkler
Example 6: A sprinkler system on a farm is set to spray water over a distance of 35 meters and
to rotate through an angle of 140. Find the area of the region.
Independent Practice
Convert from degrees to radians: Round to three decimal places
a. 115°
b. -216.35°
c. 532°
d. -48.27°
Convert from radians to degrees: Round to three decimal places
𝜋
a. 7
5𝜋
c. 11
b.
d.
15𝜋
8
13𝜋
2
Find the Arc Length on a circle
a. Radius = 15 inches, Central Angle = 180°
b. Radius = 9 feet, Central Angle = 60°
Find the Area of the Sector of the circle
a. Radius = 2.5 feet, Central Angle = 225°
a. Radius = 1.4 cm, Central Angle = 330°