Concept
Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330°, and 390° are all coterminal
To find a coterminal angle, for an angle greater than 360 you keep subtracting 360 until you get a number less than 360 or you subtract a multiple of 360 from the angle.
a) an angle between 0° and 360° that is coterminal with 1170°
= 1170 - 360
= 810 - 360
= 450 - 360
= 90
90 is an angle between 0 and 360 that is coterminal with 1170
method 2
= 1170 - 3(360)
= 1170 - 1080
= 90
b) an angle between 0° and 360° that is coterminal with 1971°
= 1971 - 360
= 1611 - 360
= 1215 - 360
= 891 - 360
= 531 - 360
= 171
171 is an angle between 0 and 360 that is coterminal with 1971
method 2
= 1971 - 5(360)
= 1971 - 1800
= 171