Trigonometry week 1

Trigonometry
Week 1

1. Point, lines, segments and rays

Point

A point is a location in space. Points are dimensionless. That is, a point has no width, length, or height. We locate pointsrelative to some arbitrary standard point, often called the "origin". Many physical objects suggest the idea of a point. Examples include the tip of a pencil, the corner of a cube, or a dot on a sheetof paper.

Line

In geometry a line:

• Is straight (no curves),
• Has no thickness.
• Extends in both directions without end (infinitely).

Line segment

A line segment is aconnected piece of a line. It has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment.

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Midpoint

A midpointof a line segment is the halfway point, or the point equidistant from the endpoints

[pic]

R is the midpoint of QS because QR = RS or because QR = ½ QS or RS = ½ QS

Ray

A ray is also apiece of a line, except that it has only one endpoint and continues forever in one direction. It could be thought of as a half-line with an endpoint. It is named by the letter of its endpoint and anyother point on the ray. The symbol → written on top of the two letters is used to denote that ray.

[pic]

2. Angles
An angle is a measure of the amount of rotation between two line segments. The2 line segments (or rays) are named the initial side and terminal side as shown in the diagram.
If the rotation is anti-clockwise, the angle is positive. Clockwise rotation gives a negative angle (byconvention).
[pic]
Examples:

[pic] Anti-clockwise, positive angle.

[pic]Clockwise, negative angle.
Angle Measurement
When measuring angles a particular angle is fixed and is taken as a unitof measurement , so that any other angle is measured by the number of times it contains the unit.
There are three major system of measurement. They are:
1. Sexagesimal System (English system)...