6.1 Positive and Negative Angles - SPM Additional Mathematics

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°

(c) \frac{22}{9} π radians

(d) \frac{10}{3} π radians

(e) –60^o

(f) –500°

(g) - 3 \frac{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)

\frac{22}{9} π rad = (2 π + \frac{4}{9} π) rad = 360^{o} + 80^{o}

Based on the above circular diagram, the positive angle of

\frac{22}{9} π radians

is in the first quadrant.

(d)

\frac{10}{3} π rad = (3 π + \frac{1}{3} π) rad = 540^{o} + 60^{o}

Based on the above circular diagram, the positive angle of

\frac{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 \frac{1}{4} π rad = (- 3 π - \frac{1}{4} π) rad = - 540^{o} - 45^{o}

Based on the above circular diagram, the negative angle of

- 3 \frac{1}{4} π radians

is in the second quadrant.