Coterminal Angles
Trigonometry - Coterminal Angles - How it Works - Video
Model
These models shows us what terminal angles are.
Coterminal angles are angles in standard position, where the initial side is on the positive x-axis, that share a common terminal side.
The one of the left is shows us the positive angles. We start with the initial side and go counterclockwise to the terminal side. The first angle is 90°. Now we can continue and pass the terminal side and continue until we reach the terminal side again. This means that we completed a complete circle or added 360° to our first angle. So our next angle is 450°.
The one of the right is shows us the negative angles. We start with the initial side and go clockwise to the terminal side. The first angle is -270°. Now we can continue and pass the terminal side and continue until we reach the terminal side again. This means that we completed a complete circle or added -360° to our first angle. So our next angle is -630°.
Example 1
Example 1:
Here our 1st angle is 60° if we go counterclockwise or in the positive direction.
If we continue the path by crossing the terminal side and go around until we reach the terminal side again, we have our 2nd angle. Since completed one circle we added 360° to 60° to get 420° for our 2nd angle.
If we continue the path by crossing the terminal side and go around until we reach the terminal side again, we have our 3rd angle. Since completed another circle we added another 360° to 420° to get 780° for our 3rd angle.
Example 2
Example 2:
Here our 1st angle is -150°, if we go clockwise or in the negative direction.
If we continue the path by crossing the terminal side and go around until we reach the terminal side again, we have our 2nd angle. Since completed one circle we added -360° to -150° to get -510° for our 2nd angle.
If we continue the path by crossing the terminal side and go around until we reach the terminal side again, we have our 3rd angle. Since completed another circle we added another -360° to -510° to get -870° for our 3rd angle.