Directions: Read carefully! Do not assume diagrams are drawn to scale.
Radian Conversions:
1.
What is the radian measure of an angle containing 60º ?
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2.
What is the radian measure of the angle formed by the hands of a clock at 2:00 p.m.?
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3.
Convert 72º to radians.
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4.
Convert 2π/3 to degree measure.
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5.
A central angle of 4π/15 radians intercepts an arc whose degree measure is _____.
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Arc Length and Radians:
1.
A child pushes a playground merry-go-round so handle A moves to position B. The radius of the merry-go-round is 4.5 feet and the central angle has a radian measure of π/3.
Find the length of minor arc to the nearest tenth of a foot.
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2.
A horse on a lunge line travels in a circle around its trainer. The radius of the horse's circle is 24 feet. If the measure of the angle between location S and P on the circle is (counterclockwise) (7π)/9 radians.
Find the distance the horse travels on the circle from S to P in feet, to the nearest foot.
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3.
A sprinkler head is equidistant from flower garden A and a small shrub B. The sprinkler waters in a circular pattern. If the length of minor arc is 12 feet and the radius of the circle is 10 feet, find the measure of the central angle subtended by minor arc in radian measure.
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4.
A circular sprinkling system can be set to water only a sector of the circle. The radius of the sector is 20 feet and its central angle measures 1 radian. What is the length of the arc formed by this sector, in feet?
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5.
A circular pizza is divided into eight equal slices. The outer edge of the crust from one piece measures 5.5 inches.
a) What is the measure, in radians, of the central angle of one pizza slice?
b) What is the diameter of the pizza to the nearest inch?
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