Transcript To find a coterminal angle

Unit 4:
Intro to Trigonometry
Trigonometry
The study of triangles and the
relationships between their sides
and angles
Let’s look at an angle in standard position, where the
initial side is ALWAYS on the positive x-axis and the
vertex is at the origin. The terminal side can be
anywhere and defines the angle.
A positive angle is described
by starting at the initial side
and rotating
counterclockwise to the
terminal side (angle ).
A negative angle is
described by rotating
clockwise (angle ).
terminal
side
vertex


initial
side
Depending upon the degree measure of the angle, the
terminal side can land in one of the four quadrants.
Angles can be larger than 360º
by simply wrapping around the
quadrants again.
(450º, 540º, 630º, 720º, etc.)
II
I
III
IV
-270
I
II
I
II
90
-360
-180
360
180
IV
III
-90
III
270
Name the quadrant of the terminal side.
1)
2)
3)
4)
5)
6)
140o
315o
-168o
475o
-340o
670o
II
IV
III
II
I
IV
I
7) 80o
8) -475o III
IV
9) -25o
10) 1030o IV
11) -1030o I
12) -225o II
Coterminal Angles are angles that share the same
terminal side, but have different angle measures.
Angles  and  are
coterminal since they share
the same sides.
There are also several other
angles that are coterminal to  .


To find a coterminal angle:
add or subtract 360º (or any multiple of 360o)
to the given angle .
Example:
= 35º
35 + 360 = 395º
35 – 360 = -325º
Both are
coterminal
angles to 
Find a negative and positive coterminal angle to -425o
Find one positive and one negative
coterminal angle for each angle below.
1) 140o
7) 80o
2) 315o
8) -475o
3) -168o
9) -25o
4) 475o
10) 1030o
5) -340o
11) -1030o
6) 670o
12) -225o