Reference Angles

[Jessica]

Standard position: An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side. If the terminal side of an angle lies "on" the axes (such as 0º, 90º, 180º, 270º, 360º ), it is called a quadrantal angle. The angle shown at the right is referred to as a Quadrant II angle since its terminal side lies in Quadrant II.




The angle is measured by the amount of rotation from the initial side to the terminal side. If measured in a counterclockwise direction the measurement is positive. If measured in a clockwise direction the measurement is negative. (A negative associated with an angle's measure refers to its "direction" of measurement, clockwise.)

If two angles in standard position have the same terminal side, they are called coterminal angles.




Reference Angles: Associated with every angle drawn in standard position (except quadrantal angles) there is another angle called the reference angle. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Reference angles may appear in all four quadrants. Angles in quadrant I are their own reference angles.