Chapter 10

1. $\begin{array}{l} \begin{array}{rcl} y & = & - 3 \sin (4 π x - π / 3) \\ a & = & - 3, b = 4 π, c = - π / 3 & amplitude = | - 3 | = 3 \end{array} \\ \begin{array}{l} period = \frac{2 π}{4 π} = \frac{1}{2} & displacement = - \frac{- \frac{π}{3}}{4 π} = \frac{1}{12} \end{array} \end{array}$
2. $\begin{array}{l} y = 0.5 \cos \frac{π}{2} x \\ Amp . = 0.5, disp . = 0, \\ per . = \frac{2 π}{π / 2} = 4 \end{array}$

x 0 1 2 3 4

y 0.5 0 $- 0.5$ 0 0.5
3. $y = 2 + 3 \sin x$

For $y_{1} = 3 \sin x,$

$\begin{array}{rcl} amp . & = & 3, per . = 2 π, \\ disp . & = & 0 \end{array}$

x 0 $\frac{π}{2}$ $π$ $\frac{3 π}{2}$ $2 π$

$y_{1} = 3 \sin x$ 0 3 0 $- 3$ 0

$y = 2 + 3 \sin x$ 2 5 2 $- 1$ 2
4. $\begin{array}{l} y = 3 \sec x \\ \sec x = \frac{1}{\cos x} \end{array}$

1-1 Full Alternative Text
5. $\begin{array}{l} y = 2 \sin (2 x - \frac{π}{3}) \\ Amp . = 2, per . = \frac{2 π}{2} = π \\ disp . = - - π / ... \end{array}$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans

`x`	0	1	2	3	4
`y`	0.5	0	$- 0.5$	0	0.5