Trigonometry
Chapter 1
1.1 Angles
Basic Terminology
Line
Ray
An Angle is formed by rotating a ray around its endpoint.
negative angle
positive angle
Basic Terminology
The ray in its initial position is
called the initial side
Terminal side
of the angle.
Vertex A
Initial side
The ray in its location after the rotation is called
the terminal side of the angle.
The endpoint of the ray is the vertex of the
angle.
Basic Terminology
The most common unit for measuring
angles is the degree.
To use degree measure, we assign 360
degrees to a complete rotation of a ray.
1/360 of a
complete rotation
A complete rotation
Basic Terminology
Acute angle: An angle measuring
between 0 and 90 degrees. 0  x  90
Right angle: An angle measuring exactly
90 degrees.
Obtuse angle: An angle measuring more
than 90 degrees but less than 180
degrees. 90  x  180
Straight angle: An angle measuring
exactly 180 degrees.
Basic Terminology
Angles

Acute

Right

Obtuse

Straight
We will use the Greek letter theta , along with
many others to name each angle.
Basic Terminology
Some Greek Letters:
Lower case:
Alpha:  Beta:  Delta: 
Sigma: 
Pi:

Lambda:
 Epsilon:

Rho:

Upper case:
Alpha:  Beta: 
Pi: 
Lambda: 
Delta:  Sigma: 
Epsilon:  Rho: 
Basic Terminology
Complementary Angles: two positive
angles whose sum is 90 degrees.
Supplementary Angles: two positive
angles whose sum is 180 degrees.
Example: Solve for m.
(5m)
(4m)
(3k )
(7k )
Basic Terminology
Standard Position
An angle is in standard position if its vertex is at the
origin and its initial side is along the positive x-axis.
y
Q1
Q2
Terminal side
90    180
Q1
0    90
x
vertex
Initial side
Q3
180    270
Q4
270    360
Basic Terminology
Coterminal angles are angles that have the same
terminal side. The measure of their angles differ by
multiples of 360 degrees. To find coterminal angles just
add or subtract multiples of 360 degrees.
y
y
420
250
60
x
Coterminal
angles
(positive)
110
x
Coterminal
angles
(negative)
Basic Terminology
Examples:
The answer for smallest positive coterminal angles must be 0    360
Find the angles of smallest possible positive measure
coterminal with each angle.
(a) 1200
(b) 75
1200  360  840
still greater than 360
840  360  480
still greater than 360
480  360  120 ans.
this answer is less than
360 so it is the final ans.
since this angle is negative
and we need the smallest positive
coterminal angle, we add multiples
of 360
75  360  285 ans.
Basic Terminology
Sometimes it is necessary to find an expression that will
generate all angles coterminal with a given angle. If we
let n represent the multiple of 360 degrees then the
expression that will generate all coterminal angles is:
x  n 360
If n is 1, we are adding 360 degrees.
If n is 2, we are adding 720 degrees.
If n is -1, we are subtracting 360 degrees, etc.
Basic Terminology
Questions?
Homework:
– Read section 1.3
– Complete assignment 1.1, due next class
– Be prepared for daily points and vocabulary
quizzes.