y = a sin(bx + c)
b = period
-c/b = positive phase shift.
c/b = negative phase shift
a --> changes amplitude of the sin function, it can stretch, compress or invert the graph in vertical direction.
if a >1 then graph stretches vertically
if a=1 ; no change is observed vertically.
if 0<a<1; graph is squeezed vertically.
if a<0 ; graph is reflected along x-axis
b --> graph is compressed or expanded or inverted horizontally.
if b >1 then graph squeed horizontally, or in another words shorten the period by factor of b
if b=1 ; no change is observed horizontally.
if 0<b<1; graph is stretched horizontally, or increases the period by the factor of b.
if b<0 ; graph is reflected along y-axis
Note: since sin function is an odd function, therefore reflecting along x-axis or y-axis will produce same result.
c--> moves graph right or left. by the amount of (c/b)
c>0 moves the graph to left
c=0 no shift
c<0 moves graph to the right.