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Master Course Outline
MATH& 142
Precalculus II

Credits: 5
Clock Hours per Quarter: 50

AA Discipline: [Quantitative] [Natural Sciences]

Lecture Hours:50

The second course of the precalculus sequence. Graphical analysis of concepts is emphasized through the use of technology. Topics include unit circle and triangle trigonometry, algebraic and graphical analysis of trigonometric and inverse trigonometric functions, applications of trigonometric functions, vectors, parametric equations, polar coordinates, and optional conic sections. Prerequisite: Grade of C- or higher in MATH& 141 or permission of the Mathematics Department. Formerly MATH 110, Precalculus II.

Intended Learning Outcomes
  • Analyze the following families of functions. Special attention should be give to analyzing their properties including, but not limited to, domains, ranges, periodicity, roots, shape, and graphical properties.
    a. Trigonometric functions: sine, cosine, tangent, arcsine, arccosine, and arctangent.
  • Successfully apply the following actions to functions from each family listed above both in an algebraic context as well as graphical context.
    a. The arithmetic operations addition, subtraction, multiplication, and division.
    b. Function composition.
    c. Transformations and translations of the type A f(B x + C) + D where f is a function from the families listed above and A,B,C, & D are real numbers.
  • Solve equations and inequalities graphically and/or algebraically which include functions from the families listed above. Graphical techniques should include both (1) intersections of f(x) + left side and g(x) = right side and (2) finding roots numerically of h(x) = (left side) - (right side).
  • Work successfully with right triangles and their applications using the trigonometric functions.
  • Use the Law of Sines and Law of Cosines to work successfully with oblique triangles and their applications.
  • Work successfully with trigonometric identities: Pythagorean identities, cofunction identities, addition and subtraction identities, double-angle identities, and one-half angle identities. Use these core identities in rewriting expressions and verifying general identities.
  • Successfully implement right triangle trigonometry in the context of two-dimensional vectors and techniques.
  • Solve systems of linear and nonlinear equations using appropriate algebraic, graphical and matrix techniques.
  • Work successfully with conic sections (parabola, circles, ellipses, and hyperbolas).
  • Successfully graph and analyze two-dimensional parametric equations.
  • Successfully graph and analyze polar equations utilizing polar coordinates for the plane.
  • Graphing calculator skills integrated into the course include, but are not limited to the following:
    a. Finding a viewing window giving the complete graph a function by zooming in and/or out as needed. Changing viewing window coordinates manually is also necessary.
    b. Using the trace feature to read coordinates from a graph.
    c. Finding x-intercepts using the built-in numerical root routine of the calculator.
    d. Plotting multiple functions and determining intersections.
    e. Plotting parametric equations.
    f. Plotting polar equations.
    g. Understand how to draw an accurate sketch of the graph of a function using the graph displayed by the calculator.
    h. Understand the limitations of calculator drawn graphs; especially in the context of domains and ranges.

  • Syllabi Listing See ALL Quarters
    Year Quarter
    MATH& 142
    Spring 2014
    Julianne Sachs
    MATH& 142
    Spring 2013
    Gary Owsley
    MATH& 142
    Winter 2013
    Michael Shively
    MATH& 142
    Winter 2010
    Gary Owsley
    MATH& 142
    Summer 2009

    Two Year Projected Schedule

    Year One* Year Two**

    *If fall quarter starts on an odd year (2003, 2005, etc.), it's Year One.
    If fall quarter starts on an even year (2002, 2004, etc.), it's Year Two.