Chapter 12.9, Problem 51SR

a.

To determine

To identify the vertical shift, amplitude, period, and phase shift of the graph.

Explanation of Solution

Given:

The given function that models the data is $y=164\cdot \left[\sin \left(x-{90}^{°}\right)\right]+164$ .

Calculation:

The general form of trigonometric equation is given as follows-

  $y=a\sin \{b(\theta -h)\}+k$

Comparing the equation $y=164\cdot \left[\sin \left(x-{90}^{°}\right)\right]+164$ with the above equation,

The amplitude $a=164$

Period is $\frac{{360}^{\circ }}{\left|b\right|}=\frac{{360}^{\circ }}{\left|1\right|}={360}^{\circ }$

The phase shift of the graph is $h={90}^{\circ }$

b.

To determine

To write an equation using the sine that models the position of a rider on the Vienna Giant Ferris Wheel in Austria, with a diameter of $200$ feet.

Answer to Problem 51SR

  $y=100\cdot \left[\sin \left(x-{90}^{°}\right)\right]+100$

Explanation of Solution

Given:

The given function that models the data is $y=164\cdot \left[\sin \left(x-{90}^{°}\right)\right]+164$ .

Calculation:

The equation using the sine that models the position of a rider on the Vienna Giant Ferris Wheel in Austria, with a diameter of $200$ feet is as follows-

  $\begin{array}{l}y=\frac{200}{2}\cdot \left[\sin \left(x-{90}^{°}\right)\right]+\frac{200}{2}\\ y=100\cdot \left[\sin \left(x-{90}^{°}\right)\right]+100\end{array}$ .