Technical Mathematics, Sixth Edition

Chapter 15. Trigonometric, Parametric, and Polar Graphs

OBJECTIVES When you have completed this chapter you should be able to Graph the sine wave, by calculator or manually. Find the amplitude, period, frequency, and phase shift for a sine wave. Find roots or instantaneous values on a sine wave. Write the equation of a given sine wave. Graph and analyze a sine wave as a function of time. Graph the cosine, tangent, cotangent, secant, and cosecant functions. Graph the inverse trigonometric functions. Graph parametric equations. Graph points and equations in polar coordinates. Convert between polar and rectangular form.

So far we have dealt with curves that rise, or fall, or perhaps rise and fall a few times. Now we will introduce curves that oscillate, repeating the same shape indefinitely, the periodic functions. These are the sort of curves we find in alternating current, or the mechanical vibrations that could cause a bridge to collapse. We find periodic motion in mechanical devices, such as the pistons in an automobile engine, the motions of the celestial bodies, sound waves, and in radio, radar, and television signals. Periodic signals are crucial to the operation of many of the exciting technological devices of the twenty-first century, from computers to satellite telephones.

In this chapter we give a small introduction to the world of periodic functions. Our main focus will be on the sine function, which has wide applications to alternating current, mechanical vibrations, and so ...