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Elementary Functions

Course Number: MTH 112
Transcript Title: Elementary Functions
Created: September 1, 2012
Updated: June 19, 2015
Total Credits: 5
Lecture Hours: 50
Lecture / Lab Hours: 0
Lab Hours: 0
Satisfies Cultural Literacy requirement: No
Satisfies General Education requirement: Yes
Grading options: A-F (default), P-NP, audit
Repeats available for credit: 0
Approved delivery mode:

Prerequisites

MTH 111, RD 115, and WR 115, or equivalent placement

Course Description

Investigates periodic functions, trigonometric identities, vectors, polar coordinates, parametric equations, complex numbers and applications. Graphing calculator required. Prerequisite: MTH 111 or equivalent placement test scores. Audit available.

Intended Outcomes

Upon successful completion of this course, students will be able to:

  1. Recognize periodic phenomena in which trigonometric functions can aid in overall understanding.
  2. Construct appropriate models using periodic functions.
  3. Recognize applications in which vectors, polar coordinates, parametric equations or complex numbers can aid in overall understanding.
  4. Accurately compute results through the appropriate use of technology and algebra.
  5. Analyze and effectively communicate results within a mathematical context.

Alignment with Institutional Core Learning Outcomes

In-depth 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

In-depth

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

In-depth

3. Apply the knowledge, skills and abilities to enter and succeed in a defined profession or advanced academic program. (Professional Competence)

Not Addressed

4. Appreciate cultural diversity and constructively address issues that arise out of cultural differences in the workplace and community. (Cultural Awareness)

In-depth

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

Outcome Assessment Strategies

At least one project plus some combination of the following:

  • Class participation
  • Group projects
  • Presentations
  • Portfolios
  • Research papers
  • Homework assignments
  • Written paper
  • Quizzes
  • Exams
  • Other assessments of the instructors choosing 

Course Activities and Design

This course will be delivered through a combination of lecture and student activities including group and individual problem solving during class. Emphasis is to be given to applications from outside the mathematics classroom. Applications will come from the broadest possible range of disciplines. 

Course Content (Themes, Concepts, Issues and Skills)

  1. Unit Circle Trigonometry
    1. Unit Circles
    2. Angles
    3. Circles, Triangles, Sine and Cosine
    4. The Other Trigonometric Functions
    5. Reference Angles.
  2. Periodic Functions
    1. Sinusoidal Graphs
    2. Graphs of the Other Trig Functions
    3. Inverse Trig functions
    4. Trig Identities
    5. Modeling.
  3. Further Applications
    1. Non-right triangles: Law of Sines and Cosines
    2. Polar Coordinates and Complex Numbers
    3. Parametric Equations
    4. Vectors and their Applications

Department Notes

Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project.