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# Circular funcions

### Formula

Theorems/Properties | Formulas/Definitions |
---|---|

Cosine. | cos(u) = x. domain: |R. range: [-1, 1]. period: 2*pi. |

Sine. | sin(u) = y. domain: |R. range: [-1, 1]. period: 2*pi. |

Secant. | sec(u) = 1/x. domain: u not = {pi/2 + k*pi}. range: (-@, -1]U[1,@). period: 2*pi. |

Cosecant. | csc(u) = 1/y. domain: u not = {pi*k}. range: (-@,-1]U[1,@). period: 2*pi. |

Tangent. | tan(u) = y/x. domain: u not = {pi/2 + k*pi}. range: |R. period: pi. |

Cotangent. | cot(u) = x/y. domain: u not = {k*pi} range: |R. period: pi. |

Reference angle theorem. | Let's i be the reference angle of u. sec(u) = -/+ sec(i), csc(u) = -/+ csc(i), tan(u) = -/+ tan(i), cot(u) = -/+ cot(i). |

Pythagorean identities. | sec²(u) - tan²(u) = 1. csc²(u) - cot²(u) = 1. |

Beyond unit circle. | L(x,y) and r= sqrt(x² + y²). sec(u) = r/x and csc(u) = r/y. |

Trigonometric functions features. | A: amplitude. period: (2*pi)/(omega). phase shift: - (phi)/(omega). phase: phi. vertical shift: B |

Periodicity. | The period of a function is the smallest value p such as: f(x + p) = f(x). |

Created by:
JuniorDBlackbone