Chapter 6.6, Problem 12E

(a)

To determine

To find: The model for the average monthly temperature in Buffalo.

Answer to Problem 12E

The model for the average monthly temperature in Buffalo is $-\frac{2\pi }{3}$ .

Explanation of Solution

Given information:

The given function is ${47.5}^0$ the temperature fluctuates ${23.5}^0$ and $t=1$ .

Calculation:

Calculate the values.

  $\begin{array}{c}h=47.5\\ A=23.5\\ \frac{2\pi }{k}=12\\ k=\frac{\pi }{6}\end{array}$

Calculate the model for the average monthly temperature in Buffalo.

  $\begin{array}{c}-\frac{c}{\frac{\pi }{6}}=4\\ c=-\frac{2\pi }{3}\end{array}$

Therefore, the model for the average monthly temperature in Buffalo is $-\frac{2\pi }{3}$ .

(b)

To determine

To find: The average temperature in March.

Answer to Problem 12E

The average temperature in March is ${35.8}^0$ .

Explanation of Solution

Given information:

The given function is ${47.5}^0$ the temperature fluctuates ${23.5}^0$ and $t=1$ .

Calculation:

Calculate the function

  $\begin{array}{c}y=23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)+47.5\\ =23.5\sin \left(\frac{\pi }{6}\times 3-\frac{2\pi }{3}\right)+47.5\\ =35.75\approx {35.8}^0\end{array}$

Therefore, the average temperature in March is ${35.8}^0$ .

(c)

To determine

To find: The average temperature in August.

Answer to Problem 12E

The average temperature in August is ${67.9}^0$ .

Explanation of Solution

Given information:

The given function is ${47.5}^0$ the temperature fluctuates ${23.5}^0$ and $t=1$ .

Calculation:

Calculate the function

  $\begin{array}{c}y=23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)+47.5\\ =23.5\sin \left(\frac{\pi }{6}\times 8-\frac{2\pi }{3}\right)+47.5\\ ={67.9}^0\end{array}$

Therefore, the average temperature in August is ${67.9}^0$ .