4.1 Radian and Degree Measure
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Transcript 4.1 Radian and Degree Measure
4.1
Radian and Degree
Measure
Initial side
Coterminal Angles Angles that differ by multiples
of 360 degrees or 2 radians.
Find a positive and negative coterminal angle
for each of the following.
13
a.
6
3
b.
4
13
13 12
2
6
6
6
11 5
,
4
4
25 11
, ,
6 6
6
What is a radian?
3 radians
2 radians
1 radian
r=1
Complementary Angles – two angles are complementary
if their sum is 90 degrees or .
2
Supplementary Angles have a sum of 180 degrees or .
Find the complementary and supplementary angles for
2
2
5 4
5
2
5
10
10
10
2
5 2 3
5
5
5
5
Conversions:
Radians
Degrees
To convert degrees to radians, multiply by
rad
180
180
To convert radians to degrees, multiply by
rad
Converting an angle from D M ' S " to decimal form.
152 15'29"
15 29
152
60 3600
152.25806
Arc Length
s r
s = arc length
r = radius
theta = radian measure
s
60
r = 4 in.
First, we need to convert degrees to radians.
4
s 4
inches 4.1888 inches
3
3
Area of a Sector of a Circle
1 2
A r
2
where
is measured in radians
A sprinkler on a golf course fairway is set to spray water over a distance
of 70 feet and rotates through an angle of 120 degrees. Find the area of the
fairway watered by the sprinkler.
120o = how many radians?
2
120
radians
3
120
70 ft
1
2 2 4900
2
A 70
5131ft
3
2
3
79-99 odd, 107
Linear and Angular Speeds
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 v of the particle is
Linear speed v
arc length s
time
t
Moreover, if
is the angle (in radian measure) corresponding to the arc
length s, then the angular speed
(the lowercase Greek letter omega)
of the particle is
central angle
Angular speed
time
t
A relationship between linear speed and angular speed is
v r
Finding Linear Speed
The second hand of a clock is 10.2 cm long. Find the linear speed of the
Tip of the second hand as it passes around the clock face.
Linear speed v
Arc length s
arc length s
time
t
2r 2(10.2) 20.4 cm
s 20.4 cm
,v
=1.068 cm/sec
t
60 sec