MAC 1114 - Trigonometry

Mathematics Department

Credit(s): 3
Contact Hours: 47
Effective Term Spring 2024 (630)

Requisites

Prerequisite MAC 1105 with a minimum grade of C or
Prerequisite MAC 1106 with a minimum grade of C or
Prerequisite Appropriate score on the SPC mathematics placement test or
Permission of the Program

Course Description

This course is a study of trigonometry with an emphasis on circular functions. Major topics include: trigonometric functions, their properties and graphs; inverse trigonometric equations; solutions of triangles; complex numbers; vector algebra; parametric equations; polar coordinates; applications. 47 Contact hours. (Note: Credit is only given for MAC 1114 or MAC 1147.)

Learning Outcomes and Objectives

  1. 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.
  2. 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 real world problems using 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.
  3. 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.
  4. The student will apply critical thinking and problem-solving strategies related to trigonometry by:
    1. proving trigonometric identities.
    2. using trigonometry formulas including sum and difference, double angle, half – angle, product – to – sum and sum - to - product.
    3. solving applications that involve circles, including the area of a sector and the arc length.
    4. solving applications that involve right triangles.
    5. solving applications that require the use the Law of Sines and/or Law of Cosines.
    6. solving science-related applications, including simple harmonic motion, linear speed, angular speed, resultant force and direction angle.
    7. solving work-related applications using vectors.

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 DBT 4/18/85 Effective Session 19851 SCN change 1/17/86 Effective Session 19871 3 YR C&I Review 1992-93 DBT 11/17/93 Effective Sess. I, l9941 C & I 11/25/97; DBT 12/15/97 Effective Session 19981 C&I 10/23/01, BOT 11/20/01, Effective yrtr 20021. C&I 4/13/04, BOT 5/21/04, Effective 20041. Flex Access 20041(0340). eff20072(0390). C&I Approval: 11/13/2007, BOT Approval: 12/17/2007, Effective Term: Spring 2008 (390).
C&I Approval: 07/21/2023, BOT Approval: 09/19/2023, Effective Term: Spring 2024 (630)

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