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# Chapter 6 Vocab

### Notes

Term | Definition |
---|---|

Sine | In a right triangle, it is the ratio of the opposite leg to the hypotenuse. |

Cosine | In a right triangle, it is the ratio of the adjacent leg to the hypotenuse. |

Tangent | In a right triangle, it is the ratio of the opposite leg to the adjacent leg. |

Cosecant | The reciprocal of Sine. |

Secant | The reciprocal of Cosine. |

Cotangent | The reciprocal of Tangent. |

Arcsine | The inverse of Sine. |

Arccosine | The inverse of Cosine. |

Arctangent | The inverse of Tangent. |

Standard Position | The initial side lies on the positive x-axis and the vertex is at the origin. |

Radian | It is converted to degrees by multiplying by 180 degrees/Pi and is the measure of a central angle whose sides intercept an arc that is the same length as the radius of the circle. |

Periodic | A function that repeats itself on a given interval. |

Arc Length (Equation/Definition) | It is equal to the product of the measure of the radius of the circle r and the radian measure of the central angle theta that it subtends. |

Area of a Sector (Equation/Definition) | Part of a circle bounded by the central angle and the intercepted arc. It is determined by taking one half of the radius squared times theta. |

Angular Velocity (Equation/Definition) | Is the ratio of change in the central angle in radians to the time required for the change. Also represented by the Greek Letter Omega. |

Linear Velocity | Is the ratio of change in the length to the time required for the change |

Quadrantal Angle (Chapter #5) | The angles whose terminal sides lie on an axis. |

The parts to y = A sin ( k@ - c) + h | A is the amplitude, k is used to determine the period, c is used to determine the phase shift, h is used to determine the vertical shift. |

Amplitude | In a function y = A sin x, it is the absolute value of A. |

Period (Equation/Definition) | It is found by taking 2 pi/k. It is the length on the domain of the graph where the function repeats. |

Phase Shift (Equation/Definition) | A horizontal translation of a trigonometric function. It is found by taking c/k, where k >0. If c < 0, the shift is to the left. If c > 0, the shift is to the right. |

Vertical Shift | It is the value h in the equation. If h>0, the graph moves upward. If h< 0, the graph moves downward |

Dimensional Analysis | Is the process of treating unit labels as mathematical factor affected by division. |