Question

It is often the case that more than one sinusoidal function can be used to model the movement of a periodic function. Examine the example periodic function given below and determine an equation. a) Post an equation you got for the given graph. b) Create your own graph of a transformed trigonometric function and give ONE possible equation for it.

Answer 1

`\begin{gathered} a)y=-2\cos\left((8)/(5)x\right)-1 \\ b)y=-3\sin\left((4)/(3)x\right)-2 \end{gathered}`

Explanation:

The standard trigonometric function is represented by the form:

`\begin{gathered} f(x)=A\text{ trig \lparen Bx-C\rparen+D} \\ \text{ where,} \\ \text{ A= amplitude } \\ \text{ B= represents the speed of the cycle} \\ \text{ Period is }(2\pi)/(b) \\ (c)/(b)\text{ represents the pase shift} \\ d=\text{ represents the vertical shift} \end{gathered}`

a) Therefore, for the given graph, since it is a cosine function reflected:

`y=-2\cos\left((8)/(5)x\right)-1`

b) Now, for your own trigonometric function, do a vertical shift down 2 units of the sinusoidal function, amplitude of 3, reflect it, and let's say it has a period of 3pi/2.

`y=-3\sin\left((4)/(3)x\right)\ -2`