Trigonometric Functions and Calculus
Liberal Arts and Business Majors

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Stefan Waner and Steven R. Costenoble

Table of Contents

1. Modeling with the Sine Function Exercises
2. The Six Trigonometric Functions Exercises
3. Derivatives of Trigonometric Functions Exercises
4. Integrals of Trigonometric Functions Exercises
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Everything for Calculus


Trigonometric functions are often omitted in basic calculus courses for students not majoring in the mathematical sciences. However, the sine and cosine functions are extremely useful in modeling cyclical trends, such as the seasonal variation of demand for certain items, or the cyclical nature of recession and prosperity. The four sections we present here are designed with this in mind; we are concerned less with the geometry of triangles than on applications of the trigonometric functions in modeling real life situations.

In the first section, we focus on the use of the sine function to model cyclical phenomena, postponing the introduction of the other trigonometric functions to Section 2. Sections 3 and 4 deal with the calculus of these functions. Of particular interest is the tabular approach to integration by parts that we use to deal with integrals of products of trigonometric and exponential functions.

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Last Updated:March, 1997
Copyright © 1996 StefanWaner and Steven R. Costenoble