Terminal Sides of Angles
Positive Angles: Positive angles are angles such that their initial side is the positive x-axis and their
“terminal” side is determined by turning in a counterclockwise direction.
Negative Angles: Negative angles are angles such that their initial side is the positive x-axis and their
“terminal” side is determined by turning in a clockwise direction.
Co-Terminal Angles: are angles whose terminal sides fall on the same line.
How To:
Determine the coordinates of a point that lies on a terminal side: draw a right triangle to the x-axis and
use Pythagorean Theorem and/or SOHCAHTOA relationships to determine missing side lengths.
Determine which quadrant the terminal side on an angle will fall:
0 < angle < 90  Quadrant I
angle = 90  positive y-axis
90 < angle < 180  Quadrant II
angle = 180  negative x-axis
180 < angle < 270  Quadrant III
angle = 270  negative y-axis
270 < angle < 360  Quadrant IV
angle = 360  positive x-axis
* For angles greater than 360, you must subtract 360(or multiple) from the angle until the result is
between 0 and 360.
Find Co-Terminal Angles:
Positive Co-terminal: angle + 360
Negative Co-terminal angle: angle - 360
Special angles:
A positive 90o angle’s terminal side falls on the positive y-axis (same as a negative 270o)
A positive 180o angle’s terminal side falls on the negative x-axis (same as a negative 180o)
A positive 270o angle’s terminal side falls on the negative y-axis (same as a negative 90o)