# Derivatives of Sines and Cosines (UMAP)

### Author: C. William Stegemoller

This module consists of several units: the first unit aproximates the derivatives of trigonometric functions; in the second unit, conjectures about the derivatives are validated and applied; the third unit develops formulas for the derivatives of the other trigonometric functions.** Table of Contents:I. INTRODUCTION (CHALLENGE PROBLEMS)II. FORMULATING CONJECTURES ABOUT THE DERIVATIVES OF y = sin x AND y = cos x** 1. The Tangent Method Applied to y = sin x and y = cos x

2. Numerically Calculating Derivatives for y = sin x and y = cos x

**III. VERIFYING CONJECTURES ABOUT THE DERIVATIVES OF y = sin x AND y = cos x AND APPLYING THE RESULTS**

1. Proving the Formula for the Derivative of y = sin x

2. Derivative of y = cos x

3. When Degree Measure is Used

4. Practice Problems Involving sin u and cos u

5. Challenge Problems Revisited

**IV. DERIVATIVES OF OTHER TRIGONOMETRIC FUNCTIONS**

1. Obtaining Formulas

2. Practice Finding Derivatives

**Appendix 1. The Tangent Method for Estimating Derivatives**

Appendix 2. Rates of Change

Appendix 3. Differentiation Formulas from Calculus

Appendix 4. Derivatives of Trigonometric Functions

Appendix 2. Rates of Change

Appendix 3. Differentiation Formulas from Calculus

Appendix 4. Derivatives of Trigonometric Functions

**V. ANSWERS TO MODEL EXAMS**

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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