Coterminal Angles

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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.



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