# Curiosidade Matematica – Formulas para Calcular Senos

Manostaxx

The text that follows is owned by the site above referred.

SOURCE: http://erichware.info/en/tutorial/math/sines.htm

```                                                                __________
___     ___     ___     ___       ___     ___       /       ___
\/ 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
```