Write a sine function with a positive vertical displacement given the following information:

the amplitude is 5, the horizontal shift is 3 to the left, y−intercept is (0,−3), and the period is 6.

The sine function is a trigonometrical function that is periodic in nature (that is it repeats itself regularly at intervals after a given value). The equation of a sine function is given by:

y = Asin[B(x-C)]+D

Where A is the amplitude, B helps to calculate period (i.e. Period = 2π/B), C is the phase shift and D is the vertical shift

Given that amplitude A = 5, period = 6, hence:

B = 2π/period = 2π/6 = π/3

Since there is a horizontal shift of 3 to the left, hence C = -3.

The y intercept is (0, -3). Hence D = -3

The equation becomes:

[tex]y= 5sin[\frac{\pi}{3} (x - 3)] -3\\\\y = 5sin[\frac{\pi}{3} x - \pi] -3[/tex]

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Write a sine function with a positive vertical displacement given the following information: the amplitude is 5, the horizontal shift is 3 to the left, y−intercept is (0,−3), and the period is 6.

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Write a sine function with a positive vertical displacement given the following information:

the amplitude is 5, the horizontal shift is 3 to the left, y−intercept is (0,−3), and the period is 6.