MAC 1147 - Pre-Calculus Algebra/Trigonometry

Mathematics Department

Credit(s): 5
Contact Hours: 77
Effective Term Fall 2024 (640)

Requisites

Prerequisite High school trigonometry and
(Prerequisite MAC 1105 with a minimum grade of C or
Prerequisite Appropriate score on the SPC mathematics placement test or
Permission of the Program)

Course Description

This is an accelerated course covering the topics of both MAC 1140 and MAC 1114 in a single session and is intended primarily for the student who plans to take MAC 2311. Major topics include: polynomial, rational, exponential, logarithmic, piecewise-defined and other algebraic functions, their properties and graphs; conic sections, their properties and graphs; polynomial equations and inequalities; matrices and determinants; partial fraction decomposition; sequences and series; mathematical induction; binomial theorem and its applications; trigonometric functions, their properties and graphs; inverse trigonometric equations; solutions of triangles; complex numbers; vector algebra; parametric equations; polar coordinates; trigonometry applications. (Note: Credit is only given for MAC 1147 or MAC 1140 or MAC 1114.)

Learning Outcomes and Objectives

  1. The student will sketch various types of mathematical functions based upon their essential properties by:
    1. graphing polynomial functions.
    2. graphing rational functions.
    3. graphing exponential functions.
    4. graphing logarithmic functions.
    5. graphing the six trigonometric functions (sine, cosine, tangent, cotangent, secant and cosecant).
    6. graphing inverse trigonometric functions.
    7. graphing piecewise-defined functions.
  2. The student will apply the properties of conic sections by:
    1. graphing circles.
    2. graphing an ellipse.
    3. graphing a hyperbola.
    4. graphing a parabola.
  3. The student will apply the fundamental concepts of trigonometry by:
    1. defining the following terms through correct usage: even and odd functions, six trigonometric functions (sine, cosine, tangent, cotangent, secant and cosecant), radian measure, complex number, vector, parametric equation.
    2. deriving the domain and range of each of the six trigonometric functions.
    3. deriving the fundamental values for each of the six trigonometric functions of the angles 0,π/6,π/4,π/3,π/2, as well as their corresponding angles in the second, third, and fourth quadrants.
  4. The student will apply the properties of trigonometric functions by:
    1. converting angles between radian and degree measures.
    2. extrapolating the relationship of a circle and a right triangle in terms of the six trigonometric functions.
    3. using the properties of the six trigonometric functions to sketch their graphs.
    4. evaluating inverse trigonometric functions at the special angles.
    5. solving trigonometric equations to find general and specific solutions.
    6. solving applications involving right, acute, and oblique triangles.
    7. recognizing the properties and graphs of polar coordinates and equations.
    8. converting coordinates and equations between polar form and Cartesian coordinate form.
    9. transforming parametric equations to equations in rectangular coordinate form.
    10. graphing parametric equations.
  5. The student will differentiate the relationship between trigonometric concepts, complex numbers, and vectors by:
    1. converting complex numbers between rectangular form and trigonometric (or polar) form.
    2. determining the products, quotients, powers and roots of complex numbers.
    3. performing vector operations including addition, subtraction, scalar multiple, finding the magnitude, dot product and direction.
  6. The student will apply critical thinking and problem solving strategies by:
    1. solving and graphing polynomial and rational equations and inequalities.
    2. solving systems of equations using matrices and determinants.
    3. determining specific terms of arithmetic and geometric sequences and sums of series.
    4. using mathematical induction to prove a given statement.
    5. using the binomial theorem to expand binomials.
    6. solving application problems that involve solving a system of equations.
    7. solving application problems that involve exponential and logarithmic growth and decay.
    8. proving trigonometric identities.
    9. using trigonometry formulas including sum and difference, double angle, half-angle, product-to-sum and sum-to-product.
    10. solving applications that involve circles, including the area of a sector and the arc length.
    11. solving application problems that involve right triangles.
    12. solving applications that require the use the Law of Sines and/or Law of Cosines.
    13. solving science-related application problems, including simple harmonic motion, linear speed, angular speed, resultant force and direction angle.
    14. solving work-related applications using vectors.
    15. writing the partial decomposition of fractions.

Criteria Performance Standard

Upon successful completion of the course the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

Revised 6/30/83. Revised 8/84 . SCN change 1/17/86 . Effective Session 19871. 3 YR C&I Review 1992-93. C&I 10/22/96, Effective Session 19971. C & I 11/25/97; DBT 12/15/97 Effective Session 19981. Effective yrtr 20021. 3 Year Review 2005 eff20061(0370). 3-Year Review 2009. C&I Approval: 10/23/2001, BOT Approval: 11/20/2001, Effective Term: Fall 2006 (370).
C&I Approval: 02/17/2024, BOT Approval: 03/19/2024, Effective Term: Fall 2024 (640)

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