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Unit Circle / Circular Functions



                 terminal
                 arm/ side
                                            initial arm/ side




Let the terminal arm be "r" = 1 and rotate it once,
this results in a circle with a radius = 1 unit in length,
   Unit Circle



    Standard Position of
                                    Initial arm lays
                                    on the x-axis


                                    the origin
Coterminal Angles
angles which share the same terminal side/ arm




ex. Give two coterminal angles for 30
Measurement of Angles
                             3 Systems

               - unit symbol is
                         o


               - has no unit symbol

                             r
                        s-
                 ra diu




                                 = arc length = s




The central angle is subtended or "covered" by an arc length
(for a given radius)

1 revolution (once around) = 360

 C=2     r


 in rads =                       rads or radians
                      or 2 (3.14) = 6.28 rads
The Connection -> Rads to Degrees




Degrees           Radians
                (exact values)
Converting Degrees          Radians

Recall




ex 1) How many radian is

               (in   -terms)
ex 2) How many degrees is

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Day 1 examples

  • 1. Unit Circle / Circular Functions terminal arm/ side initial arm/ side Let the terminal arm be "r" = 1 and rotate it once, this results in a circle with a radius = 1 unit in length, Unit Circle Standard Position of Initial arm lays on the x-axis the origin
  • 2.
  • 3. Coterminal Angles angles which share the same terminal side/ arm ex. Give two coterminal angles for 30
  • 4. Measurement of Angles 3 Systems - unit symbol is o - has no unit symbol r s- ra diu = arc length = s The central angle is subtended or "covered" by an arc length (for a given radius) 1 revolution (once around) = 360 C=2 r in rads = rads or radians or 2 (3.14) = 6.28 rads
  • 5. The Connection -> Rads to Degrees Degrees Radians (exact values)
  • 6. Converting Degrees Radians Recall ex 1) How many radian is (in -terms)
  • 7. ex 2) How many degrees is