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1 Answer

y = a sin(bx + 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.


by Level 7 User (25.7k points)

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