Coterminal Angles Definition

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Coterminal angles worksheet deals with problems on coterminal angles. Angles which are drawn in standard position that share a common terminal side are called coterminal angles. It can be positive and negative. In simple words, Coterminal angles are the angles having common terminal side. 



From the figure we understood that

A ray (x-axis) where we start measuring the angles is the initial side.

A ray where we stop measuring the angle is the terminal side.

The angles 60o, -300o, 780o are all coterminal angles.


 Example 1: Find a positive and negative coterminal angle for 250 degrees.

Solution: First add 360 to 250 to get your positive Coterminal angle

=> 250+360= 610

=> Then subtract 360 from 260 to get your negative Coterminal angle.

=> 265-360= -110


Example 2: Find a positive and negative coterminal angle for 9pi.

Solution: First add 9pi to 2pi to get your positive coterminal angle.

=> 9pi+2pi=11pi

=> Then to get your negative coterminal angle, subtract 2pi from 9pi.

=> 9pi-2pi=7pi

=> this is the negative Coterminal angle.

 
 Example 3: Find angles that are coterminal with the angle 400?
  
Solution: To find positive angles that are coterminal with 400, add any multiple of 3600 with 400

=> Therefore 400 + 3600 = 4000

=> 400 + 7200 = 7600       (360 * 2 = 720)

=> 4000 and 7600 are two positive coterminal angles.

=> To find negative angles that are Coterminal with 40 degree, subtract any multiple of 3600 with 400

=> Therefore 400 - 3600 = -3200

=> 400 - 7200 =- 6800       (360 * 2 = 720)

=> -3200 and -6800 are two negative coterminal angles.

=> Likewise we can find any number of positive and negative Coterminal angles for 40 degrees.



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