Question

Please Help!! Greatly appreciated
What sine function represents an amplitude of 1, a period of 2pi, a horizontal shift of pii, and a vertical shift of -4?

Answer 1

@zepdrix

Answer 2

Hello Ms Chrissy!
Our sine function looks like this:\[\Large\rm y=A \sin\left[b(x-c)\right]+d\]Where:
\(\Large\rm A\) is the simplitude,
\(\Large\rm \frac{2\pi}{b}\) is the period,
\(\Large\rm c\) is the horizontal shift,
and \(\Large\rm d\) is the vertical shift.

Answer 3

So ummmm

Answer 4

Using that basic function, do you think you can try to plug the numbers into the correct spots? :d

Answer 5

Yes, y= sin (2pi/b(x-pi))-4

Answer 6

Oh i said that kind of confusing.. sorry sorry.\[\Large\rm period = \frac{2\pi}{b}\]So moving stuff around gives us this equation:\[\Large\rm b=\frac{2\pi}{period}\]And our period was given to be 2pi, yes?
So we'll plug that in, which will help us determine our b value,\[\Large\rm b=\frac{2\pi}{2\pi}\]

Answer 7

You determined that your A value is simply 1, good.
Looks like our b value is just 1 also, yah?
And your shifts look correct! :)\[\Large\rm y=A \sin\left[b(x-c)\right]+d\]\[\Large\rm y=1 \sin\left[1(x-\pi)\right]-4\]\[\Large\rm y=\sin(x-\pi)-4\]

Answer 8

Thank you so much for helping me understand, I didn't know it was that simple! Can you help me with another homework problem?

Answer 9

sure c: let's try another

Answer 10

Okay, What is the rate of change from x = 0 to x = pi over 2?

Answer 11

Rate of change between these two points is going to be the slope of the line that passes through them.

Answer 12

Do you remember your slope formula?

Answer 13

Okay and yes slope = y2 - y1/x2-x1

Answer 14

\[\Large\rm m=\frac{y_2-y_1}{x_2-x_1}\]
Ok good. Well we know the x values that need to use, yes?
Those shouldn't be hard to plug in.\[\Large\rm m=\frac{y_2-y_1}{\frac{\pi}{2}-0}\]What are the y coordinates though?
Can you correctly determine the y coordinate at pi/2 by looking at the graph?

Answer 15

Y=3

Answer 16

y=0

Answer 17

\[\Large\rm m=\frac{3-0}{\frac{\pi}{2}-0}=\frac{3}{\pi/2}\]Mmmm ok good good.
Do you understand how to simply this expression?
Dividing by a fraction can be a little tricky.
Did you learn "keep change flip" or something similar maybe?

Answer 18

I'm not sure. I know I keep pi