Pre-Calculus A
Name _________________________________ Hour ______
4.1.3 Worksheet (Day 3)
Arc Length: s = r θ
Angular speed: ω =
θ must be in radians!
Linear speed: v =
𝒔
𝒕
𝜽
𝒕
or
1 rev = 2π rads
𝒓𝜽
𝒕
Make sure you are showing your work!
1) Using the formula for arc length, find the central angle for the following:
Radius
Arc Length
a)
3 cm
9 cm
b)
10 inches
5 inches
c)
6 cm
3 cm
d)
5 inches
10 inches
2) Los Angeles and San Francisco are approximately 450 miles apart on the surface
of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian
measure of the central angle with its vertex at the center of the earth and Los
Angeles on one side and San Francisco on the other.
3) For each of the following:
 Convert the following to radian measure (keep answer in exact form using π)
 Draw each angle in standard position
a) 30 degrees
b) 60 degrees
c) 90 degrees
d) 270 degrees
e) 340 degrees
f) -150 degrees
4). Through how many radians does the minute hand on a clock turn during an
hour?
5) Through how many radians does the minute hand on a clock turn during a half
hour?
6) Through how many radians does the minute hand on a clock turn in 10 minutes?
7) For each radian measure below:
 Convert to degrees
 Draw the angle in standard position
a)
𝝅
b)
𝟑
e) -
𝟕𝝅
𝟔
f)
𝝅
𝟒
𝟓𝝅
𝟑
c)
g)
𝟐𝝅
𝟑
𝟕𝝅
𝟑
d)
𝟑𝝅
𝟒
h) 4π