2012

Project title:

Trigonometric functions

sly

Mathematics SL

2012

Project title:

Trigonometric functions

Mathematics SL

Introduction

The trigonometric application problems usually involves the practical problems of production, life, military, astronomy, geography and physics, the sun and the moon's gravitational seawater will occur fluctuation, a phenomenon called tidal boat at high tide, under normal circumstances, be allowed to enter fairway, near the dock, and returned to the sea at low tide after unloading, a port water depth y (m) is the time t (unit: when) function, denoted as y = f (t)

Raw data

A seasonal daily time table depth relationship:

Moment | Depth (m) |

0:00 | 5.0 |

3:00 | 7.5 |

6;00 | 5.0 |

9:00 | 2.5 |

12:00 | 5.0 |

15:00 | 7.5 |

18;00 | 5.0 |

21;00 | 2.5 |

24;00 | 5.0 |

1. Lection of a function to approximate water depth of the harbor as a function of time, given the water depth when the whole point of the approximate value (accurate to 0.001).

Moment | 0;00 | 3:00 | 6:00 | 9:00 | 12:00 | 15:00 | 18:00 | 21:00 | 24:00 |

Depth (m) | 5.0 | 7.5 | 5.0 | 2.5 | 5.0 | 7.5 | 5.0 | 2.5 | 5.0 |

With time as the x-axis, the depth as the y-axis, and to delineate the various points in the coordinate system, and is connected with a smooth curve. According to the image, you can consider using the function to find out the relationship between of painting water depth and time.

From the data and the image can be drawn:

y=A sin(ωx＋φ)+h

A =2.5

h=5

φ=0

t=12

t=2p/w=12

w=p/6

y=2.5sin (p/6) X+5

Function is y=2.5sin (p/6)X+5

We can use this function derived formula to calculate the water depth for each hour;

Moment | 0.00 | 1:00 | 2:00 | 3:00 | 4:00 | 5:00 |

Depth (m) | 5.000 | 6.250 | 7.165 | 7.500 | 7.165 | 6.250 |

Moment | 6:00 | 7:00 | 8：00 | 9.00 | 10:00 | 11:00 |

Depth (m) | 5.000 | 3.754 | 2.835 | 2.500 | 2.835 | 3.754 |

Moment | 12:00 | 13:00 | 14:00 | 15:00 | 16:00 | 17:00 |...