28.12.2021

What is the general equation of a sine function with an amplitude of 6, a period of startfraction pi over 4 endfraction, and a horizontal shift of startfraction pi over 2 endfraction?

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Step-by-step answer

09.07.2023, solved by verified expert
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  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.


What is the general equation of a sine function, №18011077, 28.12.2021 03:52
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Faq

Mathematics
Step-by-step answer
P Answered by Master

C: y = 6 \sin (8(x-\frac{\pi}{2} ))

Step-by-step explanation:

Amplitude is changed by multiplying the entire trig function by a number, by default the amplitude is 1, so multiplying by 6 is necessary; eliminate A and B

Horizontal shift is going through the x axis, so it must be subtracted from the x value. This is only seen in choice C of the remaining answers.

Calculating the period isn't necessary because we already found the right answer but in case you need it in the future; the period is by default 2pi, to get to pi/4, it had to be 8 times smaller, so multiplying x and translations on x by 8 will get you the correct period.

Mathematics
Step-by-step answer
P Answered by Master

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.


What is the general equation of a sine function with an amplitude of 6, a period of startfraction pi
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Step-by-step answer
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Step-by-step answer
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Step-by-step answer
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Step-by-step answer
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Step-by-step answer
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