ФОРМУЛЫ ДЛЯ ВЫЧИСЛЕНИЯ СИНУСОВ

Некоторые значения синусов можно вычислить через радикалы, ниже приводятся формулы для вычисления синусов углов с шагом три градуса. Данные формулы не единственно возможные, существуют другие выражения и их можно вывести.

                                                                  __________
             ___     ___     ___     ___       ___     ___       /       ___
           \/ 30 + \/ 10 - \/ 6  - \/ 2  - ( \/ 6  - \/ 2  ) * \/ 10 + \/ 20
sin(03) = -------------------------------------------------------------------
                                        16

              ____________      ___________
             /         ___     /        ___
           \/ 30 - 6*\/ 5  - \/ 6 + 2*\/ 5
sin(06) = ----------------------------------
                           8

              _________      _________
             /      ___     /      ___
           \/ 3 + \/ 5  - \/ 5 - \/ 5
sin(09) = -----------------------------
                        4

              ____________
             /         ___     ___     ___
           \/ 10 + 2*\/ 5  + \/ 3  - \/ 15
sin(12) = ---------------------------------
                          8

              _________
             /      ___
           \/ 2 - \/ 3
sin(15) = --------------
                2

              _________
             /  ___
           \/ \/ 5  - 1
sin(18) = --------------
                4

                 ____________________________________________________________
                /             _______________________________________________
               /             /                                   ____________
           \  /          \  /       ___            ___          /         ___
            \/  2 - 1/2 * \/  7 - \/ 5  + 1/2 * (\/ 5  - 1) * \/ 30 + 6*\/ 5
sin(21) = --------------------------------------------------------------------
                                            2

                ___________________________
               /               ____________
           \  /       ___     /         ___
            \/  7 + \/ 5  - \/ 30 + 6*\/ 5
sin(24) = ----------------------------------
                          4

                _________________________
               /             ____________
           \  /             /         ___
            \/  2 - 1/2 * \/ 10 - 2*\/ 5
sin(27) = --------------------------------
                         2


sin(30) = 1/2

                 ________________________________________
                /             ___________________________
               /             /               ____________
           \  /          \  /       ___     /         ___
            \/  2 - 1/2 * \/  7 + \/ 5  - \/ 30 + 6*\/ 5
sin(33) = ------------------------------------------------
                                 2

              ____________
             /         ___
           \/ 10 - 2*\/ 5
sin(36) = -----------------
                  4

                _____________________________________________
               /               ____________
           \  /               /         ___     ___     ___
            \/  2 - 1/4 * ( \/ 10 + 2*\/ 5  + \/ 3  - \/ 15 )
sin(39) = ----------------------------------------------------
                                   2

                ________________________________________________
               /                                    ____________
           \  /       ___             ___          /         ___
            \/  9 + \/ 5  -  1/2 * (\/ 5  - 1) * \/ 30 + 6*\/ 5
sin(42) = -------------------------------------------------------
                                    4

             ___
           \/ 2
sin(45) = -------
             2

                ________________________________________________
               /                                    ____________
           \  /       ___             ___          /         ___
            \/  7 - \/ 5  +  1/2 * (\/ 5  - 1) * \/ 30 + 6*\/ 5
sin(48) = -------------------------------------------------------
                                    4

                _____________________________________________
               /               ____________
           \  /               /         ___     ___     ___
            \/  2 + 1/4 * ( \/ 10 + 2*\/ 5  + \/ 3  - \/ 15 )
sin(51) = ----------------------------------------------------
                                   2

              ___________
             /        ___
           \/ 6 + 2*\/ 5
sin(54) = ----------------
                 4

                 ________________________________________
                /             ___________________________
               /             /               ____________
           \  /          \  /       ___     /         ___
            \/  2 + 1/2 * \/  7 + \/ 5  - \/ 30 + 6*\/ 5
sin(57) = ------------------------------------------------
                                 2

             ___
           \/ 3
sin(60) = -------
             2

                _________________________
               /             ____________
           \  /             /         ___
            \/  2 + 1/2 * \/ 10 - 2*\/ 5
sin(63) = --------------------------------
                         2

                ___________________________
               /               ____________
           \  /       ___     /         ___
            \/  9 - \/ 5  + \/ 30 + 6*\/ 5
sin(66) = ----------------------------------
                          4

                 ____________________________________________________________
                /             _______________________________________________
               /             /                                   ____________
           \  /          \  /       ___            ___          /         ___
            \/  2 + 1/2 * \/  7 - \/ 5  + 1/2 * (\/ 5  - 1) * \/ 30 + 6*\/ 5
sin(69) = --------------------------------------------------------------------
                                            2

              ____________
             /         ___
           \/ 10 + 2*\/ 5
sin(72) = -----------------
                  4

              _________
             /      ___
           \/ 2 + \/ 3
sin(75) = --------------
                2

                ________________________________________________
               /                                    ____________
           \  /       ___             ___          /         ___
            \/  9 + \/ 5  +  1/2 * (\/ 5  - 1) * \/ 30 + 6*\/ 5
sin(78) = -------------------------------------------------------
                                    4

                _________________________
               /             ____________
           \  /             /         ___
            \/  2 + 1/2 * \/ 10 + 2*\/ 5
sin(81) = --------------------------------
                         2

                ___________________________
               /               ____________
           \  /       ___     /         ___
            \/  7 + \/ 5  + \/ 30 + 6*\/ 5
sin(84) = ----------------------------------
                          4

                 ________________________________________
                /             ___________________________
               /             /               ____________
           \  /          \  /       ___     /         ___
            \/  2 + 1/2 * \/  7 + \/ 5  + \/ 30 + 6*\/ 5
sin(87) = ------------------------------------------------
                                 2



sin(90) = 1