Helping Mathematically Under-Prepared Students Understand the Actual Trigonometric Functions
Year: 2024
Type: conference-paper
Abstract: Making engineering education accessible to mathematically under-prepared students entering college is difficult due to the demanding mathematical requirements the major demands.One area of difficulty is understanding the trigonometric functions.Part of the problem is that the trigonometric functions seem mysterious because they are only seen as keys on a calculator.The trigonometric functions are classified as transcendental functions.A transcendental function cannot be written as a finite combination of algebraic expressions.The key word is FINITE.This fact in most cases eliminates the equation form from ever being seen by students.Students know them only by the word's sine, cosine, and tangent on a scientific calculator.Below is the actual formula for the sine function.For simplicity, only the first three terms in the series will be used.Introducing students to these formulas will give the mathematically underprepared student the hands-on feel of working with familiar functions such as linear equations.This paper is intended to help under-prepared students understand the trigonometric functions and the notation used to represent them.Most students don't realize that the f in f(x) is being replaced by sin, cos, and tan.It will then be explained that these formulas are programmed into their calculators and are accessible by the sin, cos, and tan keys on a calculator.This paper will contain an abbreviated chapter that highlights these changes and can be included in any trigonometry course.It will also list one set of variables that represent the functions.It will contain several fully worked example problems that students can use as a learning tool.The problems will contain the use of the actual functions where students only use a calculator to calculate the first three terms given in the trigonometric formulas.Note: The use of the actual trigonometric functions are used to show that you don't need a calculator, but the calculator is then used for the remainder of the course.The purpose of this paper is not to replace the calculator, but to show students that a formula can be used and this takes the mystery out of the trigonometric functions. Future Survey Data CollectionAt this point I have had considerable positive feedback on this method through verbal conversations with my students over the past 4 years.To quantify this positive verbal feedback the actual effectiveness will be measured in upcoming trigonometric classes with a student questionnaire.The questionnaire will be given at the end of the course.
DOI: 10.18260/1-2--49440
Author: Daniel Blessner
Institution: Pennsylvania State University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
SDG: Quality education
Open Access status: gold
OpenAlex ID: W4404994453