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Write a sine function that has a midline of
y=4, an amplitude of 2 and a period of
(2pi)/(7).
Answer:
f(x)=

Write a sine function that has a midline of $y=4$ , an amplitude of $2$ and a period of $\frac{2 \pi}{7}$ . $\newline$ Answer: $f(x)=$

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Write equations of cosine functions using properties

Full solution

Q. Write a sine function that has a midline of

y=4

, an amplitude of

2

and a period of

\frac{2 \pi}{7}

.

\newline

Answer:

f(x)=

Write Amplitude: Write the amplitude $A$ of the given problem. $\newline$ The amplitude is the absolute value of $A$ . $\newline$ $A = 2$
Determine Period: Determine the period $T$ . The period $T$ is given as $\frac{2\pi}{7}$ . Find the value of $B$ . The value of $B$ determines the period of the sinusoidal function. $B = \frac{2\pi}{T}$ $B = \frac{2\pi}{\left(\frac{2\pi}{7}\right)}$ $B = 7$
Find Value of B: Determine the midline $D$ . The midline is given as $y = 4$ . This is the vertical shift of the function. $D = 4$
Determine Midline: Determine the phase shift $C$ . $\newline$ Since no phase shift is mentioned, we can assume $C = 0$ .
Determine Phase Shift: Write the equation of the sinusoidal function. $\newline$ Substitute values of $A$ , $B$ , $C$ , and $D$ into $f(x) = A \sin(Bx + C) + D$ . $\newline$ $f(x) = 2 \sin(7x + 0) + 4$ $\newline$ $f(x) = 2 \sin(7x) + 4$

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