Question

What sine function represents an amplitude of 4, a period of pi over 2, no horizontal shift, and a vertical shift of −3?

Answer 1

for sin(bx) the period is found by using \[period = \frac{2\pi}{b}\]

you have the period and need to find b\[\frac{\pi}{2} = \frac{2\pi}{b}\] solve for b

Answer 2

in general, the amplitude is y = asin(x) a = amplitude. You already know the value of a.

Answer 3

for the vertical shift its y = asin(bx) + c c is the new centre of the curve. y = sin(x) is centred on y = 0. Moving down 3 it becomes centred on y = -3.
Hope it helps