November 05, 2009
4.1 Angles and Their Measure
How are angles measured?
DMS system:
1. Convert 35.7o to DMS.
2. Convert 42o30'36" to decimal form.
November 05, 2009
Read Pg. 350
Defn: Radian
A central angle of a circle has measure 1 radian if it
intercepts an arc with the same length as the radius
r
r
θ=1
r
θ = 1 radian
if arc length = radius
November 05, 2009
Activity: piece of paper, compass, string
Do Exploration 1: (pg 352)
Extension:
1. Label a point, C, on the circle where the m AOC is 2 radians.
2. Label a point, D, on the circle where the m AOD is 3 radians.
3. Label a point, E, on the circle where the m AOE is 4 radians.
5. Label a point, F, on the circle where the m AOF is 5 radians.
6. Label a point, G, on the circle where the m AOG is 6 radians.
November 05, 2009
2 radians
1 radian
3 radians
6 radians
4 radians
5 radians
November 05, 2009
Question:
About how many degrees is 1 radian?
2 radians?
3 radians?
4 radians?
5 radians?
6 radians?
November 05, 2009
2
360
2
=
r
d
d = 360 r
d = 180r
r =
d
180
Converting:
Radians to Degrees: multiply by
Degrees to Radians: multiply by
180
π
π
180
November 05, 2009
Convert to Radians.
Convert to Degrees
1. 45
1. 2 radians
2. -135
2. 6
November 05, 2009
Arc Length (Degree Measure):
s
r
θ
Arc Length (Radian Measure):
s = πrθ
180
s = rθ
November 05, 2009
Find the perimeter of a 45o slice of a large
(10 in radius) pizza.
November 05, 2009
Angular and Linear Speed
angular speed: (measured in units, like revolutions
per minute)
linear speed: (measured in units, like miles per
hour)
November 05, 2009
linear speed: (speed a particle moves along a circular path)
d=rt
s=rt
r=s
t
linear speed = s
t
angular speed: (speed at which the angle is increasing/
decreasing)
d=rt
0=rt
r = 0
t
angular speed = 0
t
November 05, 2009
Ford Taurus:
tire diameter = 26.16in
a. Find the speed of the car in mph when the wheels
are turning at 800 revolutions per minute.
November 05, 2009
nautical mile: length of 1 minute of arc along
Earth's equator
Ex. Two cities are 895 statue miles apart. How
far are they in nautical miles?