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Exact Angle - Multiples and x-y Plane
        In Degrees                  , 60 , 45 , 30




        90 - Multiples                         60 - Multiples
               o
                                       o                         o
                                    120



    o                           o
 180




                                           o                     o
                o




        45 - Multiples                          30 - Multiples
                          o
135o
                                                                     o
                                    150o




                                                                         o
                                    210o

   o                     315o
Exact Coordinates for P( )
 Recall, P( ) = (cos , sin )




P(180
x=y
                                                     1
Use a + b = c                                    =               y
                                             r


                                             x




       (-   ,    )                       (       ,           )




      (- ,- )                        (   ,-              )


Conclusion:

                P( ) = (+
                        -   ,+
                             -   )




     tan( ) = +1
              -
Conclusion:

              P( ) = (+
                      -   , +
                            -   )




                                +
                                -
1
                  1




                                   coordinates of 30




Conclusion:

              P( ) = (+
                      -   ,+
                           -   )

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Find exact coordinates for angles using trigonometric functions

  • 1. Exact Angle - Multiples and x-y Plane In Degrees , 60 , 45 , 30 90 - Multiples 60 - Multiples o o o 120 o o 180 o o o 45 - Multiples 30 - Multiples o 135o o 150o o 210o o 315o
  • 2. Exact Coordinates for P( ) Recall, P( ) = (cos , sin ) P(180
  • 3. x=y 1 Use a + b = c = y r x (- , ) ( , ) (- ,- ) ( ,- ) Conclusion: P( ) = (+ - ,+ - ) tan( ) = +1 -
  • 4. Conclusion: P( ) = (+ - , + - ) + -
  • 5. 1 1 coordinates of 30 Conclusion: P( ) = (+ - ,+ - )