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) 22 9 π radians
(d) 10 3 π radians
(e) –60o
(f) –500°
(g)3 1 4 π 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)

22 9 π rad=( 2π+ 4 9 π ) rad= 360 o + 80 o
Based on the above circular diagram, the positive angle of 22 9 π radians  is in the first quadrant.

(d)
10 3 π rad=( 3π+ 1 3 π ) rad= 540 o + 60 o
Based on the above circular diagram, the positive angle of 10 3 π 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)

3 1 4 π rad=( 3π 1 4 π ) rad= 540 o 45 o
Based on the above circular diagram, the negative angle of 3 1 4 π radians  is in the second quadrant.