Transcript 12.2 Notes

• Q: What is the greatest angle measure
you recall seeing in Geometry?
• Q: What do you think a negative angle
measure might represent?
Angles and Angle Measure
12.2
Standard position
• Here the angle is positive since
we see a counterclockwise
rotation.
• Initial side lies on pos. x-axis.
• Vertex centered at origin.
• Terminal side (blue) here is in
Quad III.
• Red arc represents angle
rotation.
Example 1
• Draw an angle with the given measure in standard
position. Then tell in which quadrant the terminal side lies.
• (a) 215o
(b) 400o
(c) -90o
d) -335o
• What would be a positive angle measure with the same
standard position as -90o ?
• How do you arrive at that measure?
Coterminal Angle:
• when two angles in standard position have
terminal sides that coincide.
**Find coterminal angles by adding or
subtracting multiples of 360o from the
original angle.
Example 2
• Find one positive and one negative angle
that are coterminal with:
• a) -100o
b) 575o
Radians
You can also measure angles in radians.
To define a radian, consider a circle with
radius r centered at the origin.
Radian: the measure of an angle in standard position whose
terminal side intercepts an arc of length r.
• Because the circumference of a circle is 2πr, there are 2π
radians in a full circle.
• 360 = 2π radians
• 180 = π radians
Example 3
Draw the angle in standard position.
Then determine which quadrant the angle lies in.
a)
2𝜋
7
b)
11𝜋
6
c)
13𝜋
4
Example 3
Draw the angle in standard position.
Then determine which quadrant the angle lies in.
d)
3𝜋
−
7
e)
11𝜋
−
8
Coterminal Angles in radians:
**Find coterminal angles by adding or
subtracting multiples of 2π from the
original angle.
Example 4
Find one positive and one negative coterminal angle.
a)
2𝜋
7
b)
7𝜋
−
6
Conversions
Example 5: Convert.
a) 320
to radians
b)

5
12
to degree.
Example 5: Convert.
c) -245
to radians
d)
3
4
to degree.
Arc Length
- Central Angle – an angle with a vertex at the
center of the circle.
Example 6
Find the length of each arc. Keep answer in terms of π.
Example 7
• The steering wheel on a monster truck has a radius of 11
inches. How far does a point on the steering wheel travel
if the wheel makes four fifths of a rotation?