Notes on Arc Lengths and
Areas of Sectors
Precalculus 5.1
5.1
Examples
Examples
II. Arc Lengths
s  r
***When using this formula, you must be in radians!!
Examples:

Find the length of the arc intercepted by a
central angle having each of the following
measures.
Examples
Word Problems
Reno, NV, is due north of Los Angeles. The latitude of
Reno is 40° N, while the latitude of Los Angeles is 34°
N. If the radius of the Earth is 6400 km, find the
north-south distance between the two cities.
Word Problems
Given the picture of the pulley with the weight,
answer the following:
How many inches will the weight rise if the pulley is
rotated through an angle of 71° 50’ ?
Remember:
s  r
PART B:
Through what angle, to the nearest minute, must the
pulley be rotated to raise the weight 6 in?
Remember:
s  r
III. Areas of Sectors
***When using this formula, you must be in radians!!
Examples
Remember:
s  r
A
r2
2
Examples
Remember:
s  r and
A
r2
2