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?
y = sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 8 sine (4 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 x) + StartFraction pi Over 2 EndFraction

Answer:

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

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.

The General equation of a sine function is f(x) = 6·sin(8(x -π/2)).

The sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.

Here, Amplitude = 6, P=π/4, and S=π/2

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))

 f(x) = 6·sin(8(x -π/2))

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

Thus, the General equation of a sine function is f(x) = 6·sin(8(x -π/2)).

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