As its name implies, it is a table where the **values of sines, cosines and tangents of the notable angles** (from 0 ° to 360 °). With it we can perform calculations in trigonometry without using a calculator.

**Trigonometric ratios of 0**°, **30****°, 60 ° and 90 °.**

Let's consider the following triangle:

Let's calculate the following values: sin (30 °), sin (60 °), cos (30 °), cos (60 °), tg (30 °), tg (60 °).

Remembering that:

- sin α = opposite leg / hypotenuse
- cos α = adjacent leg / hypotenuse
- tg α = opposite leg / adjacent leg = without α / cos α

We have:

- sin (30 °) = a / 2a = 1/2
- cos (30 °) = (a√3) / 2a = √3 / 2
- tg (30 °) = (1/2) / (√3 / 2) = 1 / √3
- sin (60 °) = (a√3) / 2a = √3 / 2
- cos (60 °) = a / 2a = ½
- tg (60 °) = (√3 / 2) / (1/2) = √3

**Trigonometric ratios of 45****°**

Now let's consider the following right triangle:

Let's calculate the values of sin (45 °), cos (45 °) and tg (45 °):

- sin (45 °) = a / (a√2) = 1 / √2
- cos (45 °) = a / (a√2) = 1 / √2
- tg (45 °) = (1 / √2) / (1 / √2) = 1

**Values of the trigonometric functions of the notable angles**

Angle | Sine | Cosine | Tangent |

0 ° | 0 | 1 | 0 |

30 ° | |||

45 ° | 1 | ||

60 ° | |||

90 ° | 1 | 0 | ∞ |

120 ° | |||

135 ° | -1 | ||

150 ° | |||

180 ° | 0 | -1 | 0 |

210 ° | |||

225 ° | 1 | ||

240 ° | |||

270 ° | -1 | 0 | -∞ |

300 ° | |||

315 ° | -1 | ||

330 ° | |||

360 ° | 0 | 1 | 0 |