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Unformatted text preview: 94 Chapter 4 • Radian Measure §4.2 Exercises
For Exercises 1-4, ﬁnd the length of the arc cut off by the given central angle θ in a circle of radius r .
2. θ = 171◦ , r = 8 m 1. θ = 0.8 rad, r = 12 cm 3. θ = π rad, r = 11 in 4. A central angle in a circle of radius 2 cm cuts off an arc of length 4.6 cm. What is the measure of
the angle in radians? What is the measure of the angle in degrees?
5. The centers of two belt pulleys, with radii of 3 inches and 6 inches, respectively, are 13 inches
apart. Find the total length L of the belt around the pulleys.
6. In Figure 4.2.5 one end of a 4 ft iron rod is attached to the center of a pulley with radius 0.5 ft.
The other end is attached at a 40◦ angle to a wall, at a spot 6 ft above the lower end of a steel wire
supporting a box. The other end of the wire comes out of the wall straight across from the top of
the pulley. Find the length L of the wire from the wall to the box. 4 4
2 40◦ 6 Figure 4.2.5 40◦ 6 Exercise 6 Figure 4.2.6 Exercise 7 7. Figure 4.2.6 shows the same setup as in Exercise 6 but now the wire comes out of the wall 2 ft
above where the rod is attached. Find the length L of the wire from the wall to the box.
8. Find the total length L of the ﬁgure eight shape
in Figure 4.2.7. (Hint: Draw a circle of radius
4 centered at A , then draw a tangent line to
that circle from B.)
9. Repeat Exercise 8 but with the circle at A having a radius of 3 instead of 2. 2 A 2 B
Figure 4.2.7 10. Suppose that in Figure 4.2.7 the lines do not criss-cross but instead go straight across, as in a
belt pulley system. Find the total length L of the resulting shape.
11. Find the lengths of the two arcs cut off by a chord of length 3 in a circle of radius 2.
12. Find the perimeter of a regular dodecagon (i.e. a 12-sided polygon with sides of equal length)
inscribed inside a circle of radius 1 . Compare it to the circumference of the circle.
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
- Fall '11