Asine function had an amplitude of 3, period of 6pi, horizontal shift of 3pi/2, & vertical shift of -1. what is the y-value of the positive function when x=2pi?

Step-by-step explanation:

f(x) = A sin (Bx - C) + D

A

amplitude of 3 is given so  3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

B

period of 6π is given so

C

D

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

Next, solve when x = 2π

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for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c