graph y = 3 sin x and y = sin 3x on the same axes.?

Question

label the graph of each function. (include amplitude and period of each). please help with this one, i really don't get how to do it! thanks!

Answer 1

amplitude of y = 3 sin(x) is 3
the period is 2*pi

the amplitude of y = sin(3x) is 1
the period it 2/3*pi

Answer 2

On your coordinate axes mark off units on the y-axis that go
from -3 to plus three. On the x-axis, mark of units that are at 0. pi,2,pi ,3pi 2 and 2pi.

Now draw the sin wave starting at the origin rising to a max value of 3 at x = pi/2, then dropping down and passing through the x-axis at x = pi, continuing downward to a minimum value of -3 at x = 3pi/2 and then starts upwards ending at a value of 0 at x = 2pi. You have just drawn the graph of y = 3sinx. It is the same as the graph of sinx except it has a max and min of 3 and -3 instead of 1 and -1. This is all due to the 3 multiplying sinx.

Now on the x- axis, Mark the following x values:
pi/6, pi/3, 2pi/3. Now draw the sin wave starting at the origin rising to a max value of 1at x = pi/6, then dropping down and passing through the x-axis at x = pi/3, continuing downward to a minimum value of -1at x = pi/2 and then starts upwards ending at a value of 0 at x = 2pi/3. You have just completed onne complete cycle of y =sin 3x. Notice that you would have to dra two more cycles to get to 2pi. So the period of y=sin3x is 1/3 the period of y= sin x. So you cans see the effect of mutiplying x by three is to divide the period (one complete cycle) by three.

Answer 3

y = 3sin x

the amplitude is 3 (the maximun value the function gets) the period is of 2pi (after you get to 2pi the sin starts repeating itself).

Y= sin3x

the amplitude is 1, it never gets above 1 or underneath -1 and the period is (2/3)*pi

Answer 4

Take some nice values of x, like 0, 30 deg, - 30, and the multiples, form a table, 1st column x, 2nd, 3 cos x, and 3rd, sin(3x). Plot them on a rectangular coordinate as usual. Hope this helps.

Answer 5

You can download and install a free graphing program (running on Windows XP)
http://www.padowan.dk/graph/

it's very easy to use. After installation,
click Insert function
at f(x) = , type 3sin(x)
click OK

click Insert function again
type sin(3x)
click OK

you 'll have 2 graphs on the same coordinate systems.

Answer 6

just graph them, easy as pi ;)