What do you remember?
Degrees vs Radians
1800
600
450
300
1500
Precalc 4.1 Radian & Degree Measure
Generate an angle by fixing one ray, called the initial side and rotating the other ray, called the terminal side, about the vertex.
An angle whose vertex is at the origin & whose initial ray is the
positive x­axis is in standard position.
TERMINAL SIDE
INITIAL SIDE
positive
counterclockwise
negative
clockwise
To measure ϑ in RADIANS, ϑ = s/r
s = arc length
r = radius
r s
COTERMINAL ANGLES ­ two angles with the same initial side & same terminal side
To find a positive coterminal angle, ADD 360
To find a negative coterminal angle, SUBTRACT 360
NAME ONE POSITIVE & ONE NEGATIVE COTERMINAL ANGLE.
52
O
317
O
­140
400
O
O
NAME ONE POSITIVE & ONE NEGATIVE COTERMINAL ANGLE.
Two angles are SUPPLEMENTS if their SUM is 180
Two angles are COMPLEMENTS if their sum is 90
o
o
Find the complement & supplement of the angle, if it exists
51
o
112 o
85 o
360 = 2π radians, 180 = π
o
o
To convert degrees to radians, = angle x π/180
Convert the degree measures to radians.
o
48
o
­130
o
420
o
To convert radians to degrees, = angle x 180 /π
o
Convert the radian measures to degrees.
π/5
­7π/8
3π/11
Decimal Degrees vs Degrees, Minutes, Seconds
Degrees, Minutes & Seconds to Decimal Degrees
Finding arc length.
A circle has radius 4 in. Find the arc intercepted by a central angle of 240o.
θ=s/r
s = rθ to use formula
First convert to radians
(240)(π/180)
then
s = rθ
240o
4 in
Finding arc length.
A circle has radius 8 cm. Find the arc intercepted by a central angle of 60o.
Find arc length with circle with r=15 cm and central angle of Linear & Angular Speed
Consider a particle moving at a constant speed along a circular arc of radius r. If s is the arc length traveled in time t, then the linear speed = arc length/ time (s/t)
If θ is the angle in radians corresponding to the arc length s, then the angular speed = central angle/time (θ/t)
Linear speed measures how fast the particle moves and angular speed measures how fast the angle changes A lawn roller with a 10­inch radius makes 1.2 revolutions per second.
Find the angular speed of the roller in radians per second.
Find the speed of the tractor pulling the roller
DMS
64o32'47"
108.12o