Transcript Slide 1

Warm Up
• How’d the test go? Better? Worse?
• Did you do anything different to study for this
test?
• How many times have you attended tutoring?
• Did you do every homework assignment for
the unit?
Basic Terms
• An angle is formed by
rotating a ray around its
endpoint.
• The ray in its starting position
is called the initial side of the
angle.
• The ray’s location after the
rotation is the terminal side
of the angle.
initial side
Basic Terms
• Positive angle: The rotation
of the terminal side of an
angle counterclockwise.
• Negative angle: The rotation
of the terminal side is
clockwise.
Example 1: Draw each angle.
A complete rotation of a ray results in an angle
measuring 360.
We don’t have to stop there!
137 more
497
altogether!
360
137 is coterminal with
497. They have the
same terminal angle! We
can keep adding or
subtracting 360 to get
more coterminal angles.
Example 2: For the angles below, find
the smallest positive coterminal angle.
(Add or subtract 360 as may times as needed to obtain an
angle with measure greater than 0 but less than 360.)
a) 1115
b) 187
a) 1115° - 360° - 360° - 360° = 35°
b) 187 + 360 = 173
What’s a radian?
• You’re used to thinking of a circle in terms of
degrees: 360° is the whole circle. 180° is half
the circle, etc...
• Radian measure is just a different way of
talking about the circle.
• Just as we can measure a football field in
yards or feet--we can measure a circle in
degrees or in radians!
Think about what the word radian
sounds like… it sounds like “radius,”
right? It turns out that a radian has a
close relationship to the radius of a
circle.
Example 3: Convert each degree measure to radians.
(a) 30°
(b) 120°
(c)  60°
  radian  
(a) 300 
  radians
 180  6

  radian 
(c)  60 


radians

3
 180 
0
(d) 270°
(e) 104 °
  radian  2
(b) 1200 
radians

 180  3
  radian  3
(d) 270 
radians

 180  2
0
  radian 
(e) 1040 
  1.815 radians
 180 
Example 3: Convert each radian measure to degrees.
(a)

3
radian
(b) 

2
radian
(c)
5
radians
6
(d) 5 radians
  180 
(a)

  60
3   
  180 
(b)  
  90
2   
5  180 
(c)

  150
6   
 180 
(d) 5 
  286.48
  
Write these down in your notes! If you memorize
them, it will make converting from radians to
degrees (and vice versa) much easier!