The graph of y = a sin ( b ( x + c))+ d transforms the graph of y= sin x in the following way:

$a$ causes a vertical stretch, shrink and/or reflection about the x endamath-axis.

amath b causes a horizontal stretch, shrink and/or reflection about the y endamath-axis.amath

c translates the graph horizontally.

d translates the graph vertically.

$a$ causes a vertical stretch, shrink and/or reflection about the x endamath-axis.

amath b causes a horizontal stretch, shrink and/or reflection about the y endamath-axis.amath

c translates the graph horizontally.

d translates the graph vertically.