# What is the value of cos 1

## Special values of the trigonometric functions

For selected angles, the values of the trigonometric functions can also be represented as root expressions.

### Table 7CGF

Degree | 0° | 30° | 45° | 60° | 90° |
---|---|---|---|---|---|

wheel | 0 | 6π | 4π | 3π | 2π |

sinx | 0 | 21 | 212 | 213 | 1 |

cosx | 1 | 213 | 212 | 21 | 0 |

tanx | 0 | 313 | 1 | 3 | n.def. |

cotx | n.def. | 3 | 1 | 313 | 0 |

### Derivation

In an equilateral triangle we find the angles 30 ° and 60 °. According to the Pythagorasa theorem, it applies2 = h2 + (2a) 2, from which h = 23 a follows. With the definition of sine and cosine we get:

sin30 ° = cos60 ° = a2a = 21

andcos30 ° = sin60 ° = ah = a23 a = 21 3

In a square with side length a, according to the Pythagorean theorem, the length of the diagonal end = 2 a. With this we get:

sin45 ° = cos45 ° = 2 aa = 21 2.

Every science needs mathematics, mathematics does not need any.

Jacob I. Bernoulli

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