# Math 330 - Trigonometry

Description: |
This course covers the fundamentals of trigonometry and its applications. Topics include degree and radian measurements of angles, right triangle trigonometry, unit circle trigonometry, graphs of trigonometric functions, algebraic manipulation and proof of trigonometric identities, inverse trigonometric functions, solving trigonometric equations, the Laws of Sines and Cosines, vectors, the polar coordinate system, and roots and powers of complex numbers (De Moivre's Theorem). |

**Learning Outcomes and Objectives Upon completion of this course, the student will be able to:**

- identify special triangles and their related angle and side measures
- define the six trigonometric functions in terms of right triangles, the rectangular coordinate system, and the unit circle
- apply the right triangle definitions of the six trigonometric functions to solve right triangles
- evaluate trigonometric functions of angles in both degrees and radians
- evaluate trigonometric functions of special angles in both degrees and radians without a calculator
- graph the basic trigonometric functions and apply changes in amplitude, period, phase shift, and vertical shift to generate new graphs
- recognize, apply, and prove trigonometric identities
- evaluate and graph inverse trigonometric functions
- solve a variety of trigonometric equations
- use the Laws of Sines and Cosines to solve oblique triangles
- solve application problems that involve right and oblique triangles
- represent a vector both graphically and in ai+bj form
- perform basic vector operations: addition, subtraction, and scalar multiplication, as well as represent these operations graphically and algebraically
- calculate powers and roots of complex numbers using De Moivre's Theorem
- convert between polar and rectangular coordinates and equations
- graph polar equations

**Course Topics The topics for this course are typically allocated as follows:**

Lec |
Topic |

2 | The rectangular coordinate system Functions and inverse functions Domain and range |

4 | Angles and degree measure Coterminal and reference angles Radian measure, arc length, area of a sector Angular and linear velocity |

4 | Right triangle definitions of the six trigonometric functions Using a calculator to find values of trigonometric functions Solving right triangles Applications involving right triangles |

4 | Special triangles and their related angle and side measures Definitions of the six trigonometric functions using the rectangular coordinate system Unit circle definitions of the six trigonometric functions Evaluating trigonometric functions of special angles (no calculator) |

6 | Graphs of basic sine and cosine functions Amplitude, period, phase shift, vertical translation Graphing functions of the form y=Asin[B(x-C)]+D and y=Acos[B(x-C)]+D Applications involving periodic phenomenon |

3 | Graphs of basic secant and cosecant functions Vertical asymptotes of secant and cosecant graphs Graphing functions of the form y=Asec[B(x-C)]+D and y=Acsc[B(x-C)]+D |

3 | Graphs of basic tangent and cotangent functions Vertical asymptotes of tangent and cotangent graphs Graphing functions of the form y=Atan[B(x-C)]+D and y=Acot[B(x-C)]+D |

6 | Fundamental trigonometric identities Simplifying trigonometric expressions using algebra and identities Proving identities Sum and difference identities for sine, cosine, and tangent Double and half-angle identities for sine, cosine, and tangent |

6 | Inverse trigonometric functions and their graphs Solving basic trigonometric equations Solving multiple-angle trigonometric equations Solving trigonometric equations that require the use of identities and algebraic manipulation Applications of trigonometric equations |

4 | Law of Sines Law of Cosines Solving oblique triangles Applications requiring the use of the Law of Sines and Cosines |

4 | Introduction to vectors Representing a vector graphically and algebraically Basic vector operations including addition, subtraction, scalar multiplication, and dot product Applications of vectors |

4 | Trigonometric form of complex numbers Finding powers and roots of complex numbers using De Moivre's Theorem Applications of De Moivre's Theorem |

4 | The polar coordinate system Converting between rectangular and polar coordinates and equations Graphing polar equations |