Coterminal Angles

Coterminal Angles Coterminal angles are the angles having common terminal side. For an angle there are two sides initial side and a terminal side. Initial side means the line where we start measuring the angle (that is x-axis). Terminal side is a line where we stop measuring the angle. Initial side and terminal side are clearly shown in the below figure. In this 30o, 360o, -330o are Coterminal angles. Now let us draw the figure:- In simple words, the angles in a standard position that are having same terminal side are called coterminal angles. To find angles coterminal with a given angle we have to add and subtract 360 degree. Here are some examples that show you how to find coterminal angles. Example 1: Among the given pairs identify coterminal angles (60, 410), (60, - 300), (60, 240), (45, 135). Solution: To find coterminal angle with a given angle we have to subtract 360 from the given angle. = Let us take first angle = 60 (from given pairs 3 pairs having first angle 60) = Now subtract 360 from 60: 60 360 = -300 = So, from the given pairs (60, - 300) is the coterminal angles pair. Example 2: Find a positive and a negative angle coterminal with a 65 angle. Solution: To find a positive and a negative angle coterminal with a 65 = We have to add and subtract 360 from a given angle = 65 360 = 295 = 65 + 360 = 425 = Therefore, 65, 295, 425 are coterminal angles.