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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:

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