(y = a sin bx)

As we know that the period for sine curve is 2π. So the relation between period (2π) and 'b' is given by

As the value of 'b' increases the period decreases.

For Example : 1) y = 2 sin 3x

Here the amplitude = a = 2

Period =$ \frac{2π}{b}$

b= 3

⇒ Period =$ \frac{2π}{3}$

So the sine curve cut the x-axis at (π/3,0), (2π/3),(π,0),...

The graph will look like

2) y = 3 sin 2x

Here the amplitude = a = 3

Period =$ \frac{2π}{b}$

b= 2

⇒ Period =$ \frac{2π}{2} = π $

So the sine curve cut the x-axis at (π/2,0), (π,0),(3π/2,0),...

3) From the given graph, find the equation.

From the above graph, we can see that the graph is increasing curve so its sine curve.

So the equation will be y = a sin bx

Now here the amplitude = a = 2

To find the period,

one sine cycle is at π, so

Period =$ \frac{2π}{b}$ = π

So b = $ \frac{2π}{π}$

b = 2

So the equation of the above graph is y = 2 sin(2x).

3) Determine the equation for the graph given below:

From the above graph, we can see that the graph is increasing curve so its sine curve.

So the equation will be y = a sin bx

Now here the amplitude = a = 1

To find the period,

Here we can not find the time period for 1 cycle.

But from the graph we can see that one and half cycle is π, so

Period =$\frac{3}{2} \times\frac{2π}{b}$ = π

So b = $ \frac{3}{2} \times\frac{2π}{π}$

b = 3

So the equation of the above graph is y = sin(3x).

2) Compare the amplitudes of y = 1/2 sin x and y = 2 sin x with the amplitude of y = sin x and sketch a graph of each on the same coordinate system for $ 0 \leq x \leq 2π $

From Graph of y equal sin bx to Home

We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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