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
    
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