1. Exact Coordinates for P( )
Recall, P( ) = (cos , sin )
P( ) for - multiples
P( ) = (0, 1)
tan =
P( ) = (-1, 0) P( ) = (1, 0)
tan = P( ) = (1, 0)
tan =
P( ) = (0, -1)
tan =
tan( ) = sin
cos
tan(0) = 0 = 0
1
tan( ) = 1 =
0
tan( ) = 0 = 0
-1
tan( ) = -1 =
0

2. For multiples of
P( ) = (- , ) P( )=( , )
tan = tan =
P( ) =( - , - ) P( )=( ,- )
tan = tan =
For tan( ) = sin( )= =1
cos( )
tan( ) = 1

3. ex. Find cos( )
sin(- )
ex. Find over the interval [0, ] if cos = - and tan > 0

4. For multiples of
P( ) = (- , ) P( ) = ( , )
tan =
tan =
P( ) = (- ,- ) P( )=( ,- )
tan = tan =
For tan( ) = sin( )= = =
cos( )

5. Finally Coordinates for - multiples
Just switch
tan( )= = coordinates of
For multiples of
P( ) = (- , ) P( ) = ( , )
tan =
tan =
P( ) = (- ,- ) P( )=( ,- )
tan = tan =

6. ex. Find sin( ) tougher:
cos(- ) sec( )
cos( )
csc(- )
sin( )

7. Assignment:
Worksheet - Locating Angles Assignment #2