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
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.