MATH 102 Chapter Notes - Chapter -: Winter Solstice, Unit Circle, Arain

• School: UBC
• Department: Mathematics
• Course: MATH 102
• Professor: Wes Mac Iejewski

Document Summary

In this chapter we will explore trigonometric functions and their properties. This important new class of functions will be introduced here; their basic properties and interconnections will be discussed. Belonging to a wider class of periodic functions, these illustrate the ideas of amplitude, frequency, period, and phase. We will nd that many cyclic phenomena can be described approximatelyby suitably adjusted basic functions such as sine and cosine. As a second theme, we return to the idea of inverse functions and show that important restric- tions must be applied to ensure the existence of an inverse, particularlyfor the trigonometric functions. Then, in the next chapter, we calculate the derivatives of trigonometric functions and show applications to rates of change of periodic phenomena or changing angles. Trigonometric functions are closely associated with angles and ratios of sides of a right- angle triangle. But they are also connected to motion of a point around a unit circle.