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Write a cosine function that has an amplitude of 2 , a midline of
y=4 and a period of 1.
Answer:
f(x)=

Write a cosine function that has an amplitude of $2$ , a midline of $y=4$ and a period of $1$ . $\newline$ Answer: $f(x)=$

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Write equations of cosine functions using properties

Full solution

Q. Write a cosine function that has an amplitude of

2

, a midline of

y=4

and a period of

1

.

\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 Midline: Determine the midline $D$ . The midline is the vertical shift of the function, which corresponds to $D$ . $D = 4$
Find Value of B: Find the value of B. $\newline$ The value of B determines the period of the sinusoidal function. The period $T$ is given by $T = (2\pi)/B$ . $\newline$ Given period $T = 1$ , we solve for B: $\newline$ $B = (2\pi)/T$ $\newline$ $B = (2\pi)/1$ $\newline$ $B = 2\pi$
Determine Phase Shift: Determine the phase shift $C$ . Since no horizontal shift is mentioned, we can assume $C = 0$ .
Write Sinusoidal Function: Write the equation of the sinusoidal function. $\newline$ Substitute values of $A$ , $B$ , $C$ , and $D$ into $f(x) = A \cos(Bx + C) + D$ . $\newline$ $f(x) = 2 \cos(2\pi x + 0) + 4$ $\newline$ $f(x) = 2 \cos(2\pi x) + 4$

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