Precalculus With Trigonometry

Catalogue Description: Pre-calculus emphasizes the notion of a function as a unifying concept for the topics of college algebra and an extension of the topics of trigonometry. The following families of functions and their characteristics are examined within this course: polynomial functions; rational functions; exponential and logarithmic functions; and trigonometric functions. Writing assignments, as appropriate to the discipline, are part of the course. Applications involving problem-solving skills will be emphasized throughout the course.The included curriculum is broken into 9 units.

Students the Course is Expected to Serve: This course is intended for students who plan to major in business, mathematics, engineering, and science.

Course Objectives:

1. Analyze the graphs of various families of functions.
2. Apply the models and characteristics of various families of functions to scenarios in order to solve real-world problems.
3. Demonstrate an understanding of trigonometric functions and their behaviors.

Student Learning Outcomes: Upon satisfactory completion of the course, students will be able to:

A. Polynomial Functions: Identify the characteristics of a quadratic function (i.e., vertex, axis of symmetry, and direction of concavity).
B. Compute roots/zeroes of a polynomial function by factoring techniques.
C. Estimate the roots/zeroes of a polynomial function using graphs.
D. Rational Functions: Simplify rational expressions using the division algorithm.
E. Identify points of discontinuity of a rational function.
F. Identify vertical/horizontal asymptotes and end behavior of rational functions.
G. Exponential and Logarithmic Functions: Define exponential and logarithmic functions.
H. Simplify exponential and logarithmic expressions using their properties.
I. Solve exponential and logarithmic equations.
J. Formulate and apply exponential and logarithmic functions to a contextual situation.
K. Trigonometric Functions: Define the sine, cosine, tangent, and secant functions and their inverses, including the unit circle definition of these functions.
L. Solve trigonometric equations.
M. Apply right-angle trigonometry to a scenario.
N. Verify trigonometric identities.
O. Identify a trigonometric function from its graph.
P. Graph a trigonometric function using its properties (e.g., periodicity, amplitude, phase shifts, etc.).
Q. Apply trigonometric functions to basic concepts of physics (e.g., velocity, pendulum movement, basic current).
R. (It is expected that the following student learning outcomes (Characteristics of Functions) will be embedded as appropriate in the study of the family of functions listed above.) Identify the domain and range of a function.
S. Determine intervals on which functions are decreasing/increasing, continuous/noncontinuous, or piecewise.
T. Identify functions from multiple sources of information (i.e., verbal descriptions, graphs, equations, and tables of values).
U. Relate the effect of transformations (i.e., translations, rescaling, or reflections) on graphs of functions and their corresponding equations.
V. Perform operations (i.e., addition, subtraction, multiplication and division) on functions, including the composition of functions.
W. Decompose a function into a composition of two or more functions.
X. Formulate and apply a function to a contextual situation.
Y. Determine the conditions under which a function has an inverse.
Z. Identify the inverse of a function from multiple representations.
AA. Reformulate a given function into various representations (i.e., verbal, graphical, algebraic, or tabular).

Topical Outline: The course will outline the following topics:

1. Functions
2. Linear Functions
3. Polynomial and Rational Functions
4. Exponential and Logarithmic Functions
5. Trigonometric Functions of Angles
6. Periodic Functions
7. Trigonometric Equations and Identities
8. Further Application of Trigonometry
9. Conic Sections
10. Nonlinear systems of equations
11. Sequences, Series, and the Binomial Theorem

A more detailed breakdown of topics and curriculum outline can be found here.