y = **a** sin(**b**x + **c**)

a= amplitude

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.