so in class today we went over some of last nights homework, and some of the homework on periodic functions a couple days before we learned sequences. the unit periodic functions, well lets say I'm the brightest in that unit. i still don't get the whole concept. so I'm going to try and explain how to answer one of the questions we did for homework.
EXAMPLE
Jud was working with a sinusoidal data, but lost all of it except for two points. A maximum point was (3, 13) and a minimum point next to it was (7, 1). Write a sinusoidal equation that matches Jud's data.
This is the sine formula
f(x) = AsinB( x - C ) + D
What does this formula mean?
"check Lamael's most recent post to find out what it means"
To help you write a sinusoidal equation, the best way is to draw what information that has been given to you.
In this question the maximum point is (3,13) and the minimum is (7,1)
what does this mean? remember in grade like 9, when the the first number would tell us the point on the X- axis and the second would be on the Y -axis? well this is exactly that.
this is how your drawing should loo
k like.
After your done that, you figure out what the sinusoidal axis is. Sinusoidal axis equals the average and that average equals out to be your D in the sine formula.
the sinusoidal axis usually lays on the y -axis creating a straight line in between the minimum and maximum point.
In this case the minimum point is 1 and the maximum is 13. Add those two numbers up and divide by 2 and you get the sinusoidal axis which is equal to 7.
So now we got the sinusoidal axis. having that we can figure out the amplitude or A in the sine formula. The amplitude is the distance from sinusoidal axis to a maximum or minimum point.
In this case, we would subtract our sinusoidal axis from a minimum or maximum point. Here, our sinusoidal axis is 7 so we subtract that from our maximum which is 13 and get a difference of 6 which is equal to our A in our sine formula.
This is how our graph looks like now.
Why does the graph look like this your wondering? remember were dealing with periodic things, so it always goes up and down at a steady pace. like a bug on a wheel.
where did the 11 come from? well on the x - axis the points are going up by 4 so you add another 4 to 7 and you get 11.
the two variables were missing now is B and C.
Lets find B. B in our sine formula is NOT the period it determines the period according to this formula.
PERIOD = 2Pi/B OR B = 2Pi/PERIOD
The period is the difference between two maximum points. In this graph the maximum points are always at 13. At point 3 on the X - Axis the graph is at its maximum point and as you keep going down the line on the X - axis to find the next maximum point you find it to be 11. The difference between 3 and 11 is 8. So our period is 8. we then plug our period into our period formula to figure out what the variable B is.
B = 2Pi/PERIOD
Then.. B= 2Pi/8
Reduced.. B = Pi/4
The last variable were missing is C. C is called the phase shift, or horizontal shift on the graph. in this case, there was no horizontal shift so we leave C as 1.
So our sinusoidal equation looks like this..
f(x) = AsinB( x - C ) + D
f(x) = 6sin(Pi/4(x-1)) + 7
Hopefully my scribe has helped some people. Doing this scribe has helped me understand the unit a little better.
PERIODIC FUNCTIONS TEST TMRW! STUDY STUDY STUDY!!!
next scribe is..
Amanda
