Question

Pre-calculus 12 Question!


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Answer 1

I have trouble understanding the graph, please explain it to me.

Answer 2

do you know how to plot the blue curve?

Answer 3

Yes, sin(pi)=0, so it passes through zero

Answer 4

I have trouble understanding the red graph

Answer 5

yes. If you memorize the sin of certain angles, you can plot them.
or use a calculator in radian mode.

Answer 6

yes

Answer 7

the red curve is sin(3x)

if you put in x=0, sin(3*0) = sin(0) and that is 0
so (0,0) is a point on the red curve

Answer 8

yes

Answer 9

another "easy" point on the red curve is at x=0.5pi
sin(3x) when x is 0.5 is sin(3*0.5pi) = sin(1.5 pi)
you can see on the blue curve that sin(1.5pi) is -1
so the point (0.5pi, -1) is on the red curve

Answer 10

so, you mean just dividing the blue radian values to find the scale which is the red one. I mean 1.5pi / 3= 0.5 pi Therefore, (0.5pi, -1) is on the right graph which is the scale. Am I right?

Answer 11

you could put in lots of x values, multiply by 3 and get their sin
and plot the points. You get the red curve.

It turns out that the red curve looks like a sin except it is squished by a factor of 3
in other words, after 3 full cycles the red curve will fill up 0 to 2pi

Or, going backwards,
pick an x value on the blue curve and read off the y value
then plot that y value at x/3 (x divided by 3). you will get the red curve

Answer 12

yes exactly

Answer 13

Yes, you got it.

the "3" in front of the x is associated with the idea of frequency.
The bigger that number, the more cycles per 2pi
if we used time instead of radians we would measure cycles per second (we use Hertz to mean cycles per second)
and kilohertz or megahertz (for radio waves)

Answer 14

I see

Answer 15

Thank you for your time :)

Answer 16

exactly

The bigger the number, the more cycles it is going to have

Answer 17

OK, but the height should go up to 1 (and down to -1)
your curves in boxes 2 and 3 are too short.

Answer 18

yes that was only a rough sketch, but you are right, they should have the same amplitude through out the 2pi