Chapter 6.6, Problem 13E

(a)

To determine

To find: The amplitude of a sinusoidal function that models the monthly temperatures.

Answer to Problem 13E

The amplitude of a sinusoidal function that models the monthly temperatures is $4$ .

Explanation of Solution

Given information:

The given table is

Jan.	Feb.	march	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
${73}^0$	${73}^0$	${74}^0$	$$${76}^0$	${78}^0$	${79}^0$	${81}^0$	${81}^0$	${81}^0$	${80}^0$	${77}^0$	${74}^0$

Calculation:

Calculate the amplitude of a sinusoidal function that models the monthly temperatures.

  $\begin{array}{c}81-73=\frac{8}{2}\\ =4\end{array}$

Therefore, the amplitude of a sinusoidal function that models the monthly temperatures is $4$ .

(b)

To determine

To find: The vertical shift of a sinusoidal function that models the monthly temperatures.

Answer to Problem 13E

The vertical shift of a sinusoidal function that models the monthly temperatures is $77$ .

Explanation of Solution

Given information:

The given table is

Jan.	Feb.	march	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
${73}^0$	${73}^0$	${74}^0$	$$${76}^0$	${78}^0$	${79}^0$	${81}^0$	${81}^0$	${81}^0$	${80}^0$	${77}^0$	${74}^0$

Calculation:

Calculate the vertical shift of a sinusoidal function that models the monthly temperatures.

  $\begin{array}{c}81+73=\frac{154}{2}\\ =77\end{array}$

Therefore, the vertical shift of a sinusoidal function that models the monthly temperatures is $77$ .

(c)

To determine

To find: The period of a sinusoidal function that models the monthly temperatures.

Answer to Problem 13E

The period of a sinusoidal function that models the monthly temperatures is $12$ months.

Explanation of Solution

Given information:

The given table is

Jan.	Feb.	march	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
${73}^0$	${73}^0$	${74}^0$	$$${76}^0$	${78}^0$	${79}^0$	${81}^0$	${81}^0$	${81}^0$	${80}^0$	${77}^0$	${74}^0$

Calculation:

The period is how often the function repeats itself which in this case is $12$ months.

Therefore, the period of a sinusoidal function that models the monthly temperatures is $12$ months.