# 6.1 Positive and Negative Angles

6.1 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°

(e) –60o
(f) –500°

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)

$\frac{22}{9}\pi \text{rad}=\left(2\pi +\frac{4}{9}\pi \right)\text{rad}={360}^{o}+{80}^{o}$
Based on the above circular diagram, the positive angle of  is in the first quadrant.

(d)
$\frac{10}{3}\pi \text{rad}=\left(3\pi +\frac{1}{3}\pi \right)\text{rad}={540}^{o}+{60}^{o}$
Based on the above circular diagram, the positive angle of  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)

$-3\frac{1}{4}\pi \text{rad}=\left(-3\pi -\frac{1}{4}\pi \right)\text{rad}=-{540}^{o}-{45}^{o}$
Based on the above circular diagram, the negative angle of  is in the second quadrant.