MMAT 3320 NOTES SECTION 10 PAGE 1
10 TRIGONOMETRIC FUNCTIONS OF TRIGONOMETRIC ANGLES
We now want to extend our concept of angle to include measures of any
number of degrees: positive, negative, or zero.
Definition: Given two rays having a common endpoint, a trigonometric
angle is the amount of rotation needed to move the first ray, called
the initial side, to the second ray, called the terminal side. A
positive angle is generated by a counterclockwise rotation; a negative
angle is generated by a clockwise rotation; a zero angle is generated
by no rotation.
Note: To specify a trigonometric angle, in addition to its sides, we need a
curved arrow extending from its initial side to its terminal side.
63°
-220°
540°
Definition: In the Cartesian plane, an angle is said to be in standard
position if its vertex is at the origin and its initial side coincides with
the positive x-axis. Angles in standard position whose terminal sides
coincide are called coterminal angles. Angles in standard position
whose terminal sides lie on one of the axes are called quadrantal
angles. Nonquadrantal angles are said to be in a certain quadrant if
their terminal sides lie in that quadrant.
EXAMPLE 1. Draw two other angles in standard position that are
coterminal with the given angle.
135°
Are these angles quadrantal? Explain.
