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Write a sine function that has a midline of
y=5, an amplitude of 2 and a period of
(2pi)/(7).
Answer:
f(x)=

Write a sine function that has a midline of $y=5$ , 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=5

, an amplitude of

2

and a period of

\frac{2 \pi}{7}

.

\newline

Answer:

f(x)=

Find Amplitude: Write the amplitude $A$ of the given problem. $\newline$ The amplitude is the absolute value of $A$ . $\newline$ $A = 2$
Calculate Period: Period = $(2\pi)/7$ . Find the value of $B$ . The value of $B$ determines the period of the sinusoidal function. $B = (2\pi) / \text{Period}$ $B = (2\pi) / ((2\pi)/7)$ $B = 7$
Determine Midline: Write the midline $D$ of the given problem. $\newline$ The midline is the vertical shift of the function. $\newline$ $D = 5$
Find Value of $C$ : Since there is no horizontal shift given, we can assume $C = 0$ .
Write Sinusoidal Function: Write the equation of the sinusoidal function. $\newline$ Substitute values of $A$ , $B$ , $C$ , and $D$ in $f(x) = A \sin(Bx + C) + D$ . $\newline$ $f(x) = 2 \sin(7x + 0) + 5$ $\newline$ $f(x) = 2 \sin(7x) + 5$

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