Section 4.1 Radian and Degree Measure
Section Objectives: Students will know how to describe an angle and toconvert between degree and radian measures.
Positive angles are
generated by
counterclockwise
rotation, and
negative angles by
clockwise rotation,
one full revolution =
radians
revolution
radians
revolution
radians
revolution
radians
and have the same
initial and terminal sides.
Such angles are coterminal
Estimate the number of degrees in the angle.
B 24.
B 26
Estimate the angle to the nearest one-half radian.
B2
B4
Determine the quadrant in which the angle lies.
B 28. (a)
(b)
B 30. (a)
(b)
Determine the quadrant in which the angle lies. (The angle is given in radian measure.)
B 6. (a)
B 8. (a)
(b)
(b)
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Sketch the angle in standard position.
B 12. (a)
B13 (b)
B 14 (b)
Determine two coterminal angles in degree measure (one positive and one negative) for the given angle.
B36. (a)
(b)
B 38. (a)
(b)
Determine two coterminal angles in radian measure (one positive and one negative) for the given angle.
16 (a)
(b)
.
Complimentary angles Supplementary angles
3
Find (if possible) the complement and supplement of the angle.
B 20. (a)
B 22. (a) 3
(b)
(b) 1.5
Express the angle in radian measure as a multiple of
(Do not use a calculator.)
B44. (a)
(b)
B46. (a)
(b)
Express the angle in degree measure. (Do not use a calculator.)
B 56. (a)
58. (a)
(b)
(b)
Convert the angle measure from degrees to radians. Round your answer to three deci- mal places.
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B48.
B 50.
Convert the angle measure from radians to degrees. Round your answer to three deci- mal places.
B 64.
B 66.
Use the angle-conversion capabilities of a graphing utility to convert the angle measure to
72. (a)
74. (a)
form.
(b)
(b)
Length of circular arc
where
is measured in radians.
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EXAMPLE 5 Finding Arc Length A circle has a radius of 4 inches. Find the length of the arc intercepted
by a central angle of
Find the angle in radians.
B76.
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
Radius r
Arc Length s
B80.
22 feet
10 feet
Find the length of the arc on a circle of radius r intercepted by a central angle
Radius r
Central Angle
B84. 9 feet
B86. 40 centimeters
radians
B88 Find the distance between the cities. Assume that earth is a sphere of radius 4000 miles and the cities are on
the same meridian (one city is due north of the other)
Johannesburg, South Africa
Jerusalem, Israel
Linear and Angular Speed Consider a particle moving at a constant speed along a circular arc of radius r. If
s is the length of the arc traveled in time t, then the linear speed of the particle is
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Moreover, if
particle is
is the angle (in radian measure) corresponding to the arc length s, the angular speed of the
EXAMPLE 7 Finding Angular and Linear Speed
A 10 inch radius lawn roller makes 1.2 revolutions per second, .
a. Find the angular speed of the roller in radians per second.
b. Find the speed of the tractor that is pulling the roller.
B 94 An earth satellite in circular orbit 1250 kilometers high makes one complete revolution every 90
minutes. What is its linear speed? Use 6400 kilometers for the radius of the earth.
B96 Circular Saw Speed The circular blade on a saw has a diameter of 7.5 inches and rotates at 2400
revolutions per minute.
(a) Find the angular speed in radians per second.
(b) Find the linear speed of the saw teeth (in feet per second) as they contact the wood being cut.
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