Chapter 11: Applications of Trigonometry

In the same way exponential functions can be used to model a wide variety of phenomena in nature, the cosine and sine functions can be used to model their fair share of natural behaviors. In section, we introduced the concept of a sinusoid as a function which can be written either in the form $C(x)=A\cos (\omega x+\varphi )+B$ for $\omega >0$ or equivalently, in the form $S(x)=A\sin (\omega x+\varphi )+B$ for $\omega >0$. At the time, we remained undecided as to which form we preferred, but the time for such indecision is over. For clarity of exposition we focus on the sine function in this section and switch to the independent variable $t$, since the applications in this section are time-dependent. We reintroduce and summarize all of the important facts and definitions about this form of the sinusoid below.