trigonometry

1. Trigonometry
Math 102
Lecture 2

2. Course Information
Course Title : Trigonometry
No. of Units : 3
Class Schedule : Saturday
7:30PM-9PM
(Thailand Time)
Venue : Zoom

3. Definitions
Trigonometry – “triangle measurement”
– branch of mathematics concerned with the
measurement of parts, sides, and angles of a triangle.
Plane Trigonometry is restricted to triangles lying in a plane.

4. 1. Trigonometric Functions
1.1 Angles and Their Measure

5. Preliminary Concepts
•Point – a position in space
– no length, width or height
•Line – an infinite collection of points that has length, but no width or
thickness
•Plane – an infinite collection of points that has length, and width but no
thickness
Types of Points
Collinear Points – three or more points that lie on the same line
Non-collinear - three or more points that do not lie on the same line

6. Preliminary Concepts
•Ray – an endpoint P on a line and all the points on the line that lie on
one side of P.
•Segment – two endpoints, such as R and T, and all the points that lie
between R and T.
Types of Lines and Planes
Parallel lines – lines in the same plane that do not intersect
Skew Lines – two non-parallel lines that do not intersect.
NOTE: Any two distinct lines in the same plane are either parallel or
intersecting

7. 1.1 Angles and Their Measure
• A ray is a directed line segment.
•An angle is the union of two rays having a common
endpoint. The endpoint is called the vertex of the angle,
and the two rays are the sides of the angle.

8. 1.1 Angles and Their Measure
•An angle is the union of two rays having a common
endpoint. The endpoint is called the vertex of the angle,
and the two rays are the sides of the angle.

9. The measure of an angle is the amount of rotation from the initial
side to the terminal side. Three systems of measuring angles: the
degree system, the revolution system and the radian system.

10. • One degree is
1
360
of a circular rotation.
• An angle measured in degrees should always include the unit “degrees”
after the number, or include the degree symbol ° .
For example, 90 degrees = 90°.
• An angle is in standard position if its vertex is located at the origin, and its initial
side extends along the positive x-axis.

11. • If the angle is measured in a counterclockwise direction from the initial side to the
terminal side, the angle is said to be a positive angle. If the angle is measured in a
clockwise direction, the angle is said to be a negative angle.