Chapter 6.4, Problem 14CFU

To determine

the equation of the cosine function.

Answer to Problem 14CFU

  $y=\pm 1.5\cos \left(0.4\theta \right)$

Explanation of Solution

Given information:

Amplitude $\left|A\right|$ = 1.5

Period = $5\pi$

Calculation:

The equation of cosine function is as follows:

  $y=A\cos k\theta$..........(1)

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

Put the values of $A\text{ and }k$ in equation (1) and solve as follows:

  $\begin{array}{l}y=\pm \left|1.5\right|\cos \left(\frac{2\pi }{\text{Period}}\theta \right)\left[\text{Put }A=\pm \left|A\right|\right]\\ y=\pm \left|1.5\right|\cos \left(\frac{2\pi }{\text{5}\pi }\theta \right)\left[\text{Put the value of period}\right]\\ y=\pm 1.5\cos \left(\frac{2}{\text{5}}\theta \right)\\ y=\pm 1.5\cos \left(0.4\theta \right)\end{array}$

Thus the expression of cosine function is $y=\pm 1.5\cos \left(0.4\theta \right)$ .