Question

i wanted to make sure that both functions are the same.

y = 2 sin (4x + pi) +3

=

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

Answer 1

sin ( theta + pi ) = - sin ( theta )

sin ( 4x + pi ) = - sin ( 4x )

2 sin ( 4x + pi ) = - 2 sin ( 4x )


2 sin (4x + pi) + 3 = - 2 sin (4x) + 3 =
3 - 2 sin (4x)

Answer 2

For the second:
y = 2 sin <b>4 ((x) + (pi/4))</b> + 3
= 2 sin <b>(x + pi)</b> + 3 , I just distributed the 4 over the bracket

so, yes, they are the same