Write a cosine function that has a midline of y=5 an amplitude of 4,a period of (pi )/(2) , and a horizontal shift of (pi )/(4) to the right. Answer Attempt 2 out of 2 f(x)=

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Answer 1

To write a cosine function with the given parameters, we need to use the general form of a cosine function:

where:-

is the amplitude-

is the frequency-

is the horizontal shift-

is the midlineGiven:- Midline:

- Amplitude: 4- Period:

- Horizontal shift:

to the rightStep 1: Determine the amplitude.The amplitude is given as 4, so

.Step 2: Determine the frequency.The period is given as

, which means the frequency is

.Step 3: Determine the horizontal shift.The horizontal shift is given as

to the right, so

.Step 4: Determine the midline.The midline is given as

, so

.Putting it all together, the cosine function is:

Simplifying the expression inside the cosine function:

Therefore, the cosine function that satisfies the given conditions is:

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