Coterminal Angles
Two angles in standard position are called coterminal angles if they have the same terminal side.
If A is the degree measure of an angle, than all angles of the form A + 360οk, where k is an integer, are coterminal with A.
If θ is the radian measure of an angle, then all angles of the form θ + 2πk, where k is an integer, are coterminal with θ.
Example:
Find one positive angle and one negative angle that are coterminal with 0ο.
Example:
Find one positive angle and one negative angle that are coterminal with 2π.
Example:
Find one positive angle and one negative angle that are coterminal with Example: Identify all angles that are coterminal with a 60ο angle.
Reference Angles
If α is a nonquadrantal angle in standard position, its reference angle is definded as the acute angle formed by the terminal side of the given angle and the x­axis.
Reference Angle Rules:
For any angle α, 0 < α < 2π, its reference angle is defined as:
1) α, when the terminal
side is in quadrant 1.
α
2) π - α, when the terminal side is in Quadrant 2.
α
3) α - π, when the terminal side is in Quadrant 3.
α
α ­ π
4) 2π - α, when the terminal side is in Quadrant 4.
α
2π­α
If the measure of α is greater than 2π, or less than 0, it can be associated with a coterminal angle of positive measure between 0 and 2π.
Example:
Find the measure of the reference angle for each angle.
Example:
Find the measure of the reference angle for each angle.
510ο
­210ο