Question

Describe the transformations on the sine curve to get the graph of y = 3sin(4x + π ).

Answer 1

here you can reverse engineer it.

we know the form
Y = A sin (2pi / per. ( x - p.s.)) + v.s.

Answer 2

so one way to do this is to rewrite the given sine function and
turn it into the form we know about, using algebra

y = 3sin(4x + pi)
y = 3sin(4x + pi ) + 0
y = 3 sin ( 4( x + pi/4) ) + 0
y = 3 sin ( 4 ( x - (-pi/4 ) ) + 0
y = 3 sin ( 2pi / (pi/2) ( x - (-pi/4) ) ) + 0

Answer 3

now it is in the form
Y = A sin (2pi / per. ( x - p.s.)) + v.s.

also note that A could be negative, in which case |A| is amplitude