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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
For multiples of




P(    ) = (-   ,      )             P(   )=( , )
           tan =                           tan =




P(    ) =( - , - )                  P(   )=( ,-    )
          tan =                            tan =


For tan(   ) = sin(       )=   =1

               cos(       )

     tan( ) = 1
ex. Find cos(      )




           sin(-       )


ex. Find   over the interval [0,   ] if cos = -   and tan > 0
For multiples of


P(   ) = (-       ,    )                    P( ) = (   ,   )
                  tan =
                                                   tan =




P(    ) = (-      ,-       )                  P(   )=(         ,-   )
           tan =                                       tan =



For tan(      ) = sin(         )=   =   =

                 cos(          )
Finally Coordinates for    - multiples




                                      Just switch
tan(   )=        =                    coordinates of




                For multiples of


P(     ) = (-    ,     )                   P( ) = (    ,     )
                      tan =
                                                     tan =




 P(    ) = (-    ,-        )                 P(      )=(     ,-   )
            tan =                                      tan =
ex. Find sin(    )        tougher:

         cos(-       )   sec(    )

         cos(    )
                         csc(-       )
         sin(        )
Assignment:
Worksheet - Locating Angles Assignment #2

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New day 5 examples

  • 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