Trigonometric Angles

    This topic explains the difference between a geometric angle and a trigonometric angle. Right angles, straight angles, and revolutions are then defined. Graphing angles in the Cartesian coordinate system is described by defining the standard position of an angle and then explaining when an angle is positive and when an angle is negative. Finally, coterminal angles are detailed.

Definition (Trigonometric Angle) Given two rays emanating from a common point (vertex), a trigonometric angle is the amount of rotation required to turn one ray (initial side) so that it coincides with the other ray (terminal side).

Definition (Trigonometric Angle) Sign Convention for Trigonometric Angle. An angle is a positive angle when the rotation is measured by counterclockwise rotation.  An angle is a negative angle when the rotation is measured by clockwise rotation.

Definition (Trigonometric Angle) Revolution. One full turn of a ray about its endpoint is called one revolution.

    It is important to realize the difference between a geometric angle and a  trigonometric angle. One geometric angle can represent more than one trigonometric angle; more to the point, one geometric angle does not uniquely determine a trigonometric angle.

Definition (Trigonometric Angle) Right Angle, Straight Angle, Coterminal Angle. An angle of revolution is called a right angle, an angle of revolution is called a straight angle, and angles with the same terminal and initial sides are called coterminal angles.

Definition (Trigonometric Angle) Standard Position of an Angle. On a Cartesian coordinate plane, a trigonometric angle is said to be in standard position when the initial side of the angle is along the positive -axis and the vertex of the angle is at the origin.  

Definition (Trigonometric Angle) Coterminal Angle. Find 3 coterminal angles to
    Solution. The angles ...  are coterminal with since they have the same terminal side which is the positive part of the -axis. The same is true for the angles ...

Definition (Trigonometric Angle) Quadrant of an Angle. The and axes of the Cartesian coordinate plane divide the plane into four regions. When and then we say the point is in the first quadrant. When and then we say that is in the second quadrant. When and then we say that is in the third quadrant, and when and then we say that is in the fourth quadrant. Every angle, in standard position, lies in one of the quadrants or lies on one of the axes.

Definition (Trigonometric Angle) Quadrantal Angle. If the terminal side of an angle lies on the -axis or the -axis then the angle is called a quadrantal angle.

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Trigonometric Angles
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/trigonometric-angles.html