1. Appendix D: Trigonometry
I. Angles
(1) An angle has two sides and a vertex.
The vertex is placed at the origin and its initial side on the positive x-axis.
A positive angle is obtained by rotating its initial side counter-clockwise until it coincides with its terminal side.
A negative angles are formed by clockwise rotation.
(2) Measured in degrees:
90o= the angle between two perpendicular lines

2. (3) Measured in radians:
A radian is the angle subtended at the center of an unit circle by an arc of the circle whose length is equal to 1 (the length of a radius). Relationship between radian and degree:
 rad =180o (*)
degree
0 30 45 60 90  
radian
0 /6 /4 /3 /  

3. II. Definition of trigonometry
Let P(x,y) be any point on the terminal side of . Let r =
the distance between P and the origin. Then we define
the following trigonometric functions:

4. Comment:
(1) To define trigonometric functions, we can choose any point P on the terminal side
(2) We measure angles in radians unless otherwise specified
(3) sin and cos are two basic trig functions because any other trig function can be expressed in terms of sin and cos

5. (5) sin,cos,sec,csc are 2 periodic functions:
(4) Since division by 0 is not defined, tan and sec are not defined when x = 0, and cot and csc are not defined when y = 0
(5) sin,cos,sec,csc are 2 periodic functions:
Reason: the angles  and  + 2 have the same terminal sides. So sin  = sin( + 2 )
(6) tan and cot are  periodic functions
Reason: If x, y are on the terminal side of , then – x, – y are on the terminal side of  +  .
So tan  = y/x = (– y )/ (– x) = tan( +  ).
Similarly, cot  = cot( +  ).

6. (7) You must memorize 
/ / / /2
sin 
cos 