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 look 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

Today's Slides: May 28

Here they are ...

Applied 40S May 28, 2009

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May 26th's and Today's Notes

As of the notes of Periodic Functions on May 26, we have learned and relearned of clarifying the amplitude, the period, and the phase shift.

To identify the amplitude, simply clarify the difference between the sinusodial axis and the maximum or mininum.

A period is determined through of the fraction 2(pi)/b. The parameter itself can be identified by switching 'b' with the period shown.









Parameter C is the phase shift. The phase shift moves the graph either left or right on the sinusodial axis, it is normally subtracted from x. The phase shift is identified as either a whole number or pi/c if the starting point value is less than a whole number.

We were also taught of the cosine function. But it bears a very close resemblence to the Sine function, so we'll only be learning of the Sine function this year. The difference from the Sine function is that it's starting point is pi/2 units apart.












For today's notes, we learn of Sequences, a list of numbers that follow a certain pattern. We learn of two types of Sequences, Recursive and Implicit. A recursive sequence, is a list of numbers generated by continuously adding the difference to the first term. Such an equation would be y= 3 ( n - 1 ) + 4, the 3 would be identified as the difference. Take note that n would be rank. An implicit sequence is basically a list of numbers generated by a linear equation. More or less y = 3 n + 1. The difference in an linear equation would be the slope.

With that said, this scribe will now bid you adieu. As he is sleep deprived, the next scribe will be Don. Please, the person that is to take care of the scribe list, please update it regularly. This is also for anyone next year as well. If, the scribe list is used again.

Today's Slides: May 27

Here they are ...

Applied 40S May 27, 2009

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Today's Slides: May 26

Here they are ...

Applied 40S May 26, 2009

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Transformation of the Sine function

Today in class, we learned what each parameter in the sine function does.

This is what a sine function formula looks like:



but.. what does the formula mean?

Let's start with Parameter D:

Parameter D shifts the graph up and down
- a (+) value shifts the graph upwards by
x number of units
- a (-) value shifts the graph downwards

so..if D = 2, the graph shifts up 2 units
if D = -2, it shifts down 2 units




Parameter A:


Parameter A controls the amplitude of
the graph

* The amplitude gets higher when the value of
gets bigger. A negative value will flip the wave
upside down, but the height of the wave does
not change.

Example:



-the black wave is what a basic
function looks like
- the blue wave represents the function with
a negative A value (A=-2)
-the red wave represents the function with a
positive A value (A= 2)

Parameter B:



Parameter controls the width of the
graph. It also multiplies the copy of
the wave.

normal sine function : period = 2π
so...B= 2 is the same as 2π/2 or π
* the value of B becomes divides the
normal sine function.

Example :



- black wave : sin(X)
- red wave : sin (2X)
Parameter C:



Parameter C shifts the graph
left and right
- a (+) value shifts the graph
to the left by x number of
units.
- a (-) value shifts the graph
to the right.

Example:


- black wave - represents the basic
sine function
- red wave - represents a positive C
value ( C=2)
- blue wave - represents a negative C
value (C= -2)

That's it for today's blog. I hope it helped you guys understand the today's topic.

The next blogger will be... Roe.

Today's Slides: May 25

Here they are ...

Applied 40S May 25, 2009

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