Since sin(-x) = -sinx , sinx is an odd function.

The value of the functions sin x repeats in every 2π units of `x` . Therefore this function is periodic with a period of

The term `a` in the general form of the sinusoidal function represents the amplitude of this function.

The amplitude is a constant for sinusoidal functions.

From the general form of sinusoidal function, the period T can be written as` T = 2π/ b

Now let us come back to the simplest sinusoidal function .

y =a sin bx

where a = amplitude .

Period = 2π / b

y = a sin (bx + c ) + d

Both b and c affect the phase shift or movement of graph

If c -----------> Positive -----------> the shift is towards right If c -----------> Negative -----------> shift is towards left. If d ----------->Positive ----------->graph shifted up by d units. If d ----------->Negative -----------> graph shifted down by d units. |

Phase shift = - c / b

Period = 2π / b

The phase shift is the amount that the curve is moved in a horizontal direction from its normal position.

Phase shift, Negative -----------> Left Displacement

Phase shift, Positive -----------> Right Displacement

To find the phase shift , just make

bx + c = 0 and solve.

y = 2 sin (2x +1 )

Here amplitude = a = 2

2x + 1 = 0 ⇒ x = -1/2 so Phase shift = -1/2.

Period = 2π / b

Period = 2π / b = 2π / 2 = π

Graph Dictionary

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers