MATH 41 COURSE DESCRIPTION: (GQ) Trigonometry and Analytic Geometry (3:3:0) Straight lines: circles; functions and graphs; graphs of polynomial and rational functions; exponential and logarithmic functions; trigonometry; conic sections. PREREQUISITES: Math 21 or satisfactory performance on the mathematics proficiency examination. TOPICS FUNCTIONS AND GRAPHS Graphs and Symmetry Equations of Lines The Definition of a Function The Graphs of a Function Techniques in Graphing Methods of Combining Functions Inverse Functions POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION Linear Functions Quadratic Functions Applied Functions: Setting up Equations Maximum and Minimum Problems Polynomial Functions Graphs of Rational Functions EXPONENTIAL AND LOGARITHMIC FUNCTIONS Exponential Functions The Exponential Function y = e^x Logarithmic Functions Properties of Logarithms Applications TRIGONOMETRIC FUNCTIONS OF ANGLES Trigonometric Functions of Acute Angles Right-Triangle Applications Trigonometric Functions of General Angles Algebra and the Trigonometric Functions The Law of Sines and the Law of Cosines TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS Radian Measure Trigonometric Functions of Real Numbers Graphs of the Sine and Cosine Functions Graphs of the Tangent and the Reciprocal Functions Identities Trigonometric Equations The Inverse of Trigonometric Functions ANALYTIC GEOMETRY The Parabola The Ellipse The Hyperbola Polar Coordinates ROOTS OF POLYNOMIAL EQUATIONS Division of Polynomials The Remainder Theorem and the Factor Theorem The Fundamental Theorem of Algebra Rational and Irrational Roots Conjugate Roots and Descartes's Rule of Signs 8/13/92