### Trigonometric Curves

The three main trigonometric graphs are:

- Sine graph
- Cosine graph
- Tan graph

#### Sine Graph

x^{0} | sin x |

0 | 0 |

90 | 1 |

180 | 0 |

270 | -1 |

360 | 0 |

**Characteristics:**

- Period is 360
^{0}. It repeats itself every 360 degrees.
- Maximum value = +1
- Minimum value = -1

#### Cosine Graph

x^{0} | cos x |

0 | 1 |

90 | 0 |

180 | -1 |

270 | 0 |

360 | 1 |

**Characteristics:**

- Period is 360
^{0}. It repeats itself every 360 degrees.
- Maximum value = +1
- Minimum value = -1

#### Tan Graph

x^{0} | tan x |

0 | 0 |

90 | ∞ |

180 | 0 |

270 | ∞ |

360 | 0 |

**Characteristics:**

- Period is 180
^{0}. It repeats itself every 180 degrees.
- Maximum value = +∞
- Minimum value = -∞

#### Practice for Trigonometric Curves - interactive

You may move the grid so that you can see the behaviour of the curves for the bigger values of the angles - on both sides.

#### Transformation of a Graph

x^{0} | sin x | 2 sin x | 1 + 2 sin x |

0 | 0 | 0 | 1 |

90 | 1 | 2 | 3 |

180 | 0 | 0 | 1 |

270 | -1 | -2 | -1 |

360 | 0 | 0 | 1 |

This is stretched by a factor 2 parallel to the y-axis and then moved up by 1 - a translation of 1 in the positive y-axis.

**Now, in order to complement what you have just learnt, work out the following questions:**

>

- Sketch the following graphs:
- 2 cos x
- 1 - 3 sin x
- 2 tan x
- 2 + 3 sin x

- Find the period, maximum value and minimum value of the following functions:
- 3 cos x
- 1 - 2sin 2x
- 3 cos 2x
- 2 + 3 sin x/2