1.1 Angles
Suggested
Calculator (may also be used for M215+)
TI-30XIIS costs about $13 at WalMart or wherever
Terminology
Line
- 
Line Segment 
Ray
Endpoint of Ray
Angle
two rays in a plane with a common endpoint know as the
vertex of the angle.
Initial Side - rotated to terminal side
Positive
angle rotate
counterclockwise
Negative
angle rotate
clockwise
Degree Measure
360 o is one complete
revolution
1 o is 
of a full circle
Right Angle - measure is 90 o
Acute Angle - measure is between 0 o
and 90 o
Obtuse Angle measure is between 90 o
and180 o
Straight Angle - measure is 180 o
is frequently used as
a symbol to name an angle
Complementary Angles - two angles whose sum is 90 degrees
Supplementary Angles two angles whose sum is 180
degrees
Examples: For
= 37o ,
find
a) the complement of
b) the supplement of
If two
complementary angles have measures of 2x
and 7x, find the angles.
If two supplementary angles have measures of 6x 4 and 8x 12, find the angles.
What is the
measure of an angle that is its own complement?
Degrees, minutes, and seconds
1 (minute)
= 
or 60 minutes = 
1 (second)
= 
= 
or 60 seconds = 1 minute
3600 seconds =
Example:
Find the complement of 72o 58 11
Converting between
degrees/minutes/seconds and decimal degrees
Convert to
nearest thousandth of a degree:
a) 34 o 51 35
b) 165 o 37 9
Convert to
degrees minutes and seconds
a) 46.75 o
b) 25.485 o
Standard Position
Initial
side is positive x-axis
Quadrantal Angle
The terminal side is on an axis: 0 o, 90 o , 180 o,
270 o, 360 o,
Co terminal Angles
If rotate more than once in positive or
negative directions
Name the
angle above as two negative co terminal angles
Name the
angle above as two positive co terminal angles
Name the angle
above in general
General
Abstract name of angle co terminal with 
+ 360n;
where n is an integer
Example
Locate the
point in a coordinate system. Draw a ray
from the origin through the given point and indicate the angle of least
positive measure. Find the distance r from the origin to the point, using
the distance formula: 
Applications
#128 A windmill makes 90 revolutions per min. How many revolutions does it make per
seconds?
#130 An airplane propeller rotates 1000 times per
min. Find the number of degrees that a
point on the edge of the propeller will rotate in 1 sec.