4.1: Radian and Degree Measure

4.1: Radian and Degree Measure - Day 1
Goals
Use radian and degree measure.
Sketch angles in standard position.
Find complements and supplements of radian measures.
Convert degrees to radians.
Convert radians to degrees.
positive angles negative angles coterminal angles labels for angles
Chapter 4 Page 1
Radian Measure
Radian measure
one radian = the angle that intercepts an arc (s) equal to one
radius (r) of the circle
or
the number of radii in the arc
More facts about radians
one full revolution =
a real number
WHY??
most of the time pi is involved
no symbol (like with degrees)
If one full revolution =
then
1/2 revolution =
1/4 revolution =
1/8 revolution =
1/6 revolution =
Chapter 4 Page 2
Radians are RAD!
What range of radian
measures are in each
quadrant?
QI:
QII:
QIII:
QIV:
Coterminal angles - same terminal sides
Example:
Chapter 4 Page 3
RADian Examples
Determine the quadrant
in which each angle lies.
Determine two coterminal angles of each angle (tip: add or subtract 2pi)
Chapter 4 Page 4
Complements, supplements, and conversions (oh, my!)
Find the complement and supplement of each angle. (if possible)
3
1.5
Converting Between Degrees and Radians
One rotation =
________ = _______
If 360o = 2pi then what does 1 degree equal in terms of radians?
If 2pi = 360o then what does 1 radian equal in terms of degrees?
To Convert:
Degrees to radians
Radians to degrees
Chapter 4 Page 5
Conversions
Convert degrees to radians (leave in terms of pi, no calculator))
Convert degrees to radians (round to three decimals)
Convert radians to degrees (no calculator)
Convert radians to degrees.
Chapter 4 Page 6
4.1 Day 1 Assignment
p.269 #7-47 odds (21 questions)
Chapter 4 Page 7
4.1 Day 1 KEY p.269 #7-47 odds
Chapter 4 Page 8

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