Write a sine function that has a midline of y=2 an amplitude of 5, a period of (5pi )/(4) , and a horizontal shift of (5pi )/(8) to the left. Answer Attemptiout of 2 f(x)=

Question

Answer 1

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

where:-

is the amplitude-

is the frequency-

is the horizontal shift-

is the midlineGiven:- Midline:

- Amplitude: 5- Period:

- Horizontal shift:

to the leftStep 1: Determine the value of

.The amplitude is given as 5, so

.Step 2: Determine the value of

.The period is given as

. The period of a sine function is given by

, so we can set up the equation:

Solving for

, we get:

Step 3: Determine the value of

.The horizontal shift is given as

to the left. This means

.Step 4: Determine the value of

.The midline is given as

, so

.Putting it all together, the sine function is:

Therefore, the sine function with the given parameters is:

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