Question

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?

Answer 1

f(x) = 6·sin(8(x -π/2))

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))

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

f(x) = 6·sin(8(x -π/2))

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Additional comment

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