Math Check

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

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  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)

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

    so, yes, they are the same

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