# Tangent Checkers!

## If you multiply a 45-degree angle by consecutive odd numbers, a checkered pattern can be made with the tangent! Check out the table below! Notice the pattern in the right column?

Angle |
[Number of Degrees] ÷ 45 |
Tangent of Angle |

45° | 1 | 1 |

135° | 3 | -1 |

225° | 5 | 1 |

315° | 7 | -1 |

405° | 9 | 1 |

495° | 11 | -1 |

585° | 13 | 1 |

675° | 15 | -1 |

765° | 17 | 1 |

855° | 19 | -1 |

945° | 21 | 1 |

1035° | 23 | -1 |

1125° | 25 | 1 |

The tangents of these angles created a checkered pattern that goes: **"+1, -1 , +1, -1, +1, -1..."!** Every 2nd odd number that multiplies the 45-degree angle gives a tangent of **-1.** (Note: If you see no plus or minus to the left a number, then it's *positive* by default.)

## And guess what: this math trick works in the *negative* direction of the number line!

Angle |
[Number of Degrees] ÷ 45 |
Tangent of Angle |

-45° | -1 | -1 |

-135° | -3 | 1 |

-225° | -5 | -1 |

-315° | -7 | 1 |

-405° | -9 | -1 |

-495° | -11 | 1 |

## What's the difference in this 2nd table? The pattern starts with -1 on the top instead of +1. Simple as that! It depends on where you start on the number line which one goes 1st on top in the table. But remember to skip every __90 degrees__ in the left column, because the *common difference* of the angle series is __90 degrees.__

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© Derek Cumberbatch