Chapter 6.4, Problem 54E

To determine

the equation of the cosine function.

Answer to Problem 54E

  $y=\pm 15\cos \left(72\pi t\right)$

Explanation of Solution

Given information:

Amplitude $\left(A\right)$ = 15

Frequency = 36 hertz

Calculation:

The equation of cosine function is as follows:

  $y=A\cos kt$...........(1)

Here $A$ is an amplitude which is an absolute value of the coefficient and $k=\frac{2\pi }{\text{Period}}$ .

The value of $k$ is evaluated as follows:

  $\begin{array}{c}k=\frac{2\pi }{\text{Period}}\\ k=\frac{2\pi }{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\text{Frequency}$}\right.\right)}\left[\because \text{Period}=\frac{1}{\text{Frequency}}\right]\\ k=2\pi \left(\text{Frequency}\right)\\ =2\pi \left(\text{36}\right)\\ =72\pi \end{array}$

The value of $k$ Is

  

Put the values of in equation (1) and solve as follows:

  

Thus the expression of cosine function is