Chapter 6.4, Problem 52E

To determine

To write: an equation for the graph.

Answer to Problem 52E

  $y=-1.5\sin \left(0.5\theta \right)$

Explanation of Solution

Given information:

  

Calculation:

The highest number in y-axis that is touched by the wave is called amplitude. For the given graph the amplitude is 1.5. Since the graph starts at zero and goes down, so it is a negative sine graph.

The period of the function is $4\pi$ . The value of k will be evaluated as follows:

  $\begin{array}{c}k=\frac{2\pi }{\text{Period}}\\ =\frac{2\pi }{4\pi }\left[\text{Put the value of period}\right]\\ =0.5\end{array}$

The value of k is 0.5.

Put the values in the function $y=-A\sin \left(k\theta \right)$ , to get the expression of sine function of the graph, i.e. $y=-1.5\sin \left(0.5\theta \right)$ .