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# Trig notes

Question | Answer |
---|---|

circumference of a circle | 2πr |

arc length in degrees | s = θ/360 (2πr ) |

arc length in radians | s = θr or θ=s/r |

area of a sector in degrees | θ/360(πr^2) |

area of a sector in radians | 1/2(θr^2) |

angular speed(angle/time) | w=θ/time (rpm x 2π = radians/min) |

linear speed(distance/time) | v = w x r |

sin60° | √3/2 |

cos30° | √3/2 |

cos60° | 1/2 |

tan60° | √3/1 |

sin30° | 1/2 |

tan30° | 1/√3 = √3/3 |

sin45° | √2/2 |

cos45° | √2/2 |

tan45° | 1 |

unit circle equation | x^2 + y^2 = 1 |

tanθ = ?/? | tanθ = sinθ/cosθ |

cotθ = ?/? | cotθ = cosθ/sinθ |

sin^2θ + cos^2θ = ? | sin^2θ + cos^2θ = 1 |

1 + tan^2θ = ? | 1 + tan^2θ = sec^2θ |

1 + cot^2θ = ? | 1 + cot^2θ = csc^2θ |

area of a triangle | 1/2(a)(b)(sinθ) |

height of a triangle | a(sinθ) |

if y=a(cos or sin)(k(x-b))+c, a = ? | amplitude |

if y=a(cos or sin)(k(x-b))+c, k = ? | period |

if y=a(cos or sin)(k(x-b))+c, b = ? | phase shift |

if y=a(cos or sin)(k(x-b))+c, c = ? | vertical shift |

period for sin(x) = y =? | 2π |

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1423555193