Chapter 5 Trigonometric Functions of Real Numbers

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Trigonometry begins with circular motion and develops into a powerful way to describe repeating patterns. This chapter introduces the unit circle and uses terminal points to define sine, cosine, tangent, and their reciprocal functions for real-number inputs. You will learn exact values, signs, identities, symmetry, and periodicity before examining the graphs of all six trigonometric functions. Transformations will reveal how amplitude, period, phase shift, midline, and asymptotes affect those graphs. The chapter concludes with sinusoidal models of simple and damped harmonic motion. These ideas provide the mathematical foundation for studying waves, sound, rotating objects, seasonal cycles, and other periodic phenomena.