# Sundry Applications and Computations of sin() & cos()

## Keywords:

Computer Architecture, Since(), Cos()## Synopsis

The application disciplines of sine and cosine functions are not only large in number but also distributed. Usually, the usages of sine and cosine functions do not play any attention for general people. To the best of my knowledge, there is no such book that describes many such applications with related computations in one place so that a student or an academician can find ample of resources. This book aims to present selected applications (by categorizing real-world and simulation) as well as computations of sine and cosine functions from miscellaneous disciplines. Predominantly, this book provides a practical, realistic understanding of many and of various types of applications as well as computations of sine and cosine functions. As it might be expected, my choice of application disciplines reflects my own predilections; quite a few other disciplines would have been selected.

This book also presents the scientific computational efforts and related results of sine and cosine functions. For example, the computation of sin(x) and cos(x) simultaneously for any real value of x takes on the average 22.5 nanoseconds for the IA-64 CPU with a clock rate of 1.0 GHz using compiler gcc but without its optimizing options, whereas standard math library takes 106.5 nanoseconds for the same specification; resulting a speedup factor of greater than 4. Basically, this book explores the breadth of the subject while including enough depth to convey a good comprehension for the application disciplines involved.

Although a significant part of this book is related to computer science and computation related things, it is a multidisciplinary book by nature. This book can be used for academic texts in numerous disciplines.

The primary audience for this book can be anyone, particularly who has ever asked the question of “Where are we ever going to apply the basic trigonometric functions?”. Such enthusiast might find this book interesting in reading. To study trigonometry (and also computer architecture) would be a confusing, painful, and joyless endeavor for many students. However, this book gives students an overview of interrelationship between the basic trigonometric functions (e.g., sine and cosine) and a wide range of academic disciplines in terms of applications and computations. Many trigonometric problems and solutions,

which we actually encounter everyday life, have been included in this book. During writing this book, it has been maintained the accessibility for both technical and nontechnical students over a wide range of disciplines as well as educational levels. Besides, it was not the target to make this book mathematical rigor, yet getting students to feel more connected to the basic trigonometric functions a bit more.

**Contents**

**Introduction****Real World Applications of Sine and Cosine Functions****Sine and Cosine Functions in Computer Simulation****Algorithms for Computing Sine and Cosine Functions****Essentials of Computer Architecture****Hardware Optimization of Sine and Cosine Functions****Software Optimization of Sine and Cosine Functions**

**Appendix A: Different Processor Architectures**

**Appendix B: Solutions to Selected Questions**

**Bibliography**