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Write the equation of a sine function that has the given characteristics.

Amplitude: 4
Period: 3pie

1 Answer

4 votes

Answer:

y = 4 sin(2x/3)

Explanation:

The parent function for sine functions is: y = a sin b(x - c) + d

"a" defines amplitude/vertical dilation

"b" defines the change to the period/horizontal dilation

"c" defines the phase shift/horizontal translation

"d" defines the midline/vertical translation

We can already set "a = 4" because 4 is the amplitude.

However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.

This means: 2π/b = period

2π/period = b

2π/3π = b

2/3 = b

Knowing the "a" and "b" values, we can set up the equation:

y = 4 sin(2x/3)

No horizontal/vertical translations were applied, so "c" and "d" are both zero.

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