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!