Two angles in standard position that share the same terminal side. Coterminal Angles Two angles in standard position that share the same terminal side. Since angles differing in radian measure by multiples of 2p, and angles differing in degree measure by 360° are equivalent, every angle has infinitely many coterminal angles.

Coterminal Angles 52° p/3 radians Use multiples of 360° to find positive coterminal angles. Use multiples of 2p to find positive co- terminal angles

Find one positive and one negative angle that are coterminal with an angle having a measure of 7p/4. + = 7p 4 p 4 - 2p - =

Find all angles that coterminal with a 60° angle. Since all angles that are multiples of 360° are coterminal with a given angle, all angles coterminal with a 60° are represented by: 60° + 360k° where k is an integer.

Reference Angles A reference angle is defined as the acute angle formed by the terminal side o the given angle and the x-axis. reference angle 218° 57° 38° 128° reference angle 52° 331° reference angle 29° reference angle

Find the measure of the reference angle for each angle. 13p 3 5p 3 5p 4 This angle is in Quadrant III so we must find the difference between it and the x-axis. - 2p - = 6p 3 5p 3 p 3 - = This angle is coterminal with 5p/3 in quad- rant IV, so we Must find the difference be- tween it and the X-axis. 5p 4 - p = 5p 4 4p 4 p 4 reference angle - = reference angle

Find the measure of the reference angle for 510° 510° is coterminal with 150°, which is in quadrant III, so we must find the difference between 150° and the x-axis. 180° - 150° = 30° reference angle