Download Trigonometry Lecture Notes, Section 3.2

Trigonometry Lecture Notes
Section 3.2
Page 1 of 4
Section 3.2: Applications of Radian Measure
Big Idea: .
Big Skill: Y.
Arc Length
The length s of the arc intercepted on a circle of radius r by a central angle of measure  radians
is given by the product of the radius and the angle measure.
s = r
Practice:
1. Find the arc length intercepted by a central angle of 38.2 in a circle of radius 15.8 cm.
2. Suppose that city A has latitude of 38N, and city B, which is due south, has latitude of
15 south. What is the distance between the cities given that the radius of the Earth is
3960 miles?
Trigonometry Lecture Notes
Section 3.2
Page 2 of 4
3. A rope is wound around a drum of radius 0.327m by rotating the drum through an angle
of 132.6. Compute the length of rope wound around the drum.
4. A small gear of radius 3.6 inches drives a larger gear of radius 5.4 inches. Find the angle
the larger gear rotates if the smaller drive gear rotates through 150.
Area of a Sector of a Circle
The area A of a sector of a circle of radius r by a central angle of measure  radians is given by:
1
A   r2
2
Trigonometry Lecture Notes
Section 3.2
Page 3 of 4
Practice:
1. Calculate the area of the sector intercepted by a central angle of 38.2 in a circle of radius
15.8 cm.
2. Calculate the area and perimeter of the shaded annular region below.
Trigonometry Lecture Notes
Section 3.2
Page 4 of 4
3. When cutting aluminum with a bandsaw, it is recommended that the blade speed be set to
750 feet per minute. At how many RPM should a bandsaw be run to cut aluminum if the
wheel of the bandsaw has a 2.5 foot diameter?
4. The picture below shows a cartoon of a drill press. The drive shaft is turned by the
electric motor and has three different pulleys attached to it. The drill shaft turns the drill
bit and also has three different pulleys on it. Which two pulleys should be connected with
a belt so that the drill shaft spins at about 500 RPM? The drive shaft spins at 360 RPM.