5.1 Positive and Negative Angles

5.1 Positive and Negative Angles
1. Positive angles are angles measure in an anticlockwise rotate from the positive x-axis about the origin, O.

2. Negative angles are angles measured in a clockwise rotation from the positive x-axis about the origin O.


3. One complete revolution is 360° or 2π radians.


Example:
Show each of the following angles on a separate diagram and state the quadrant in which the angle is situated.
(a) 410°
(b) 890°
(c)229π radians  
(d)103π radians
(e) –60o
(f) –500°
(g)314π radians

Solution:
(a)
410° = 360° + 50°
Based on the above circular diagram, the positive angle of 410° is in the first quadrant.


(b)
890° = 720° + 170°
Based on the above circular diagram, the positive angle of 890° is in the second quadrant.


(c)

229πrad=(2π+49π)rad=360o+80o
Based on the above circular diagram, the positive angle of 229π radians  is in the first quadrant.


(d)
103πrad=(3π+13π)rad=540o+60o
Based on the above circular diagram, the positive angle of 103π radians  is in the third quadrant.



(e)
Based on the above circular diagram, the negative angle of –60° is in the fourth quadrant.



(f)
–500° = –360° – 140°
Based on the above circular diagram, the negative angle of –500° is in the third quadrant.


(g)

314πrad=(3π14π)rad=540o45o
Based on the above circular diagram, the negative angle of 314π radians  is in the second quadrant.