How do you graph y equals 4 sin 3x?

Answer 1

The simplest way is to use a graphing calculator such as a TI-83.

To enter in the graph do the following...

1) Hit "Y=" (It should be located in the upper left hand corner)

2) Enter the function = 4 sin (3x)

Use the X,T,Theta,N button for "x"

3) Hit "Graph"

Please note, make sure your calculator is in Degree Mode, and the graph is set to a "Functional" graph. To check this hit the mode button.

Degree and Func should be highlighted.

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You can also draw this by hand here's how...

First you need to understand the important values of sin x

sin(0) = 0

sin(30) = ½

sin(60) = √3 / 2

sin(90) = 1

sin(120) = √3 / 2

sin(150) = ½

sin(180) = 0

These are important because they are part of the unit circle.

Notice the repeating pattern.

The important points are 0, 30, 90, 150, 180

We can plot those on a graph then we see an oscillating wave that repeats.

But this would be for ƒ(x) = sin (x)

Instead the 3x on the inside means we are looking for values which make our sin the same

We find these by dividing the special points by 3.

0,10,30,50,60

So on those x values we will put a coordinates.

Now we have to determine the y values of the coordinates.

To find these we just multiply by the coefficient 4.

4 sin (3*00) = 0

4 sin (3*10) = 4/2 = 2

4 sin (3*30) = 4

4 sin (3*50) = 4/2 = 2

4 sin (3*60) = 0

Now we have our points

(00,00)

(10,02)

(30,04)

(50,02)

(60,00)

We plot these and then connect them on a graph to create an oscillating wave...