PFP Mathematics

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PFP Mathematics 2

1. TRIGONOMETRY

1.1 Angles, Arcs and Sectors

Angles

An angle is determined by rotating a ray (half-line) about its endpoint. The initial side of an angle is the starting position of the ray. The terminal side of an angle is the position of the ray after rotation. The vertex of an angle is the endpoint of the ray (see Figure1) An angle is in standard position when the origin is the vertex and the initial side coincides with the x -axis (Figure2)

A positive angle is generated by a counter-clockwise rotation; whereas a negative angle is generated by a clockwise rotation (Figure 3) Angles that have the same initial and terminal sides (Figure 4) are referred to as co-terminal.

Units for Angle Measurements

Angles can be measured in units called the degree or the radian.

Angles with measures between 0 and π/2 radians are acute angles

Angles with measures between π/2 and π radians are obtuse angles

Angles with measures between π and 2π radians are reflex angles [Figure 8(a)]

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