## Trigonometry

**Trigonometry** derived from **Greek** word **trigonon means** **“triangle”** and **metron** means **“measure”. **Trigonometry is a branch of mathematics that deal with angles, lengths and heights of triangles and relations between different parts of circles and other geometrical figures**.** Trigonometry is the foundation of all applied geometry, including geodesy, surveying, celestial mechanics, solid mechanics, navigation.

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are **sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)**.

### Trigonometric table

The Trigonometrical ratios table helps to find the values of trigonometric standard angles such as **0°, 30°, 45°, 60° and 90°**. The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles. Another important application of trigonometric tables is for Fast Fourier Transform algorithms.

Angles (In Degrees) |
0∘ |
30∘ |
45∘ |
60∘ |
90∘ |
180∘ |
270∘ |
360∘ |

sin |
0 | 12 | 12–√ | 3–√2 | 1 | 0 | −1 | 0 |

cos |
1 | 3–√2 | 12–√ | 12 | 0 | −1 | 0 | 1 |

tan |
0 | 13–√ | 1 | 3–√ | Not Defined | 0 | Not Defined | 1 |

cot |
Not Defined | 3–√ | 1 | 13–√ | 0 | Not Defined | 0 | Not Defined |

csc |
Not Defined | 2 | 2–√ | 23–√ | 1 | Not Defined | −1 | Not Defined |

sec |
1 | 23–√ | 2–√ | 2 | Not Defined | −1 | Not Defined | 1 |