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.

Compound Interest

Today, we learned how to calculate Compound Interest problems.

Compound Interest
is a system which adds the accumulated interest to the principal, such that the interest earned is based on that adjusted principal.

Here's the formula for calculating Compound Interest and what it means.





A = final amount at the end of the term
P = principle amount
1 = preserves original investment
r = rate in decimal number
n = number of times compounded
t = time in years

Knowing the formula, we can now calculate Compound Interest.

Here's an example.

Justin decided to invest $1000 for 2 years. The bank told him that the interest rate will be 5.25% and will be compounded semi-annually. How much will Justin end up with after 2 years?

Solution:







TVM (Time Value Money) solver does all the calculation for us. Here's what a TVM solver screen look like.




N = time x number of times compounded
I% = interest rate in %
PV = present value
PMT = payment made to the account
FV = Future Value
P/Y = # of payments per year
C/Y = # of times compounded per year


the next scribe will be....


Jason. :)

Reflection on Statistics

There had been a lot of complications about this unit. Today, I finally understood what each command does. We did a lot of calculations and analyzed datas. It was pretty confusing at first. Especially for those who does not pay attention. I find binomial distribution easier than normal distribution. The invNorm command still confuses me sometimes. I'm not sure when to shade right or left. Besides that, I think I understand most of it.

Tomorrow will be our Unit Test. Good luck to everyone.

Probability : randBin

Hi everyone! We didn't really learn anything new today. It was basically just
a review of the pasts lessons and homeworks. Today's post will be about randBin.
Most people are having troubles understanding how randBin works, including
myself, but I tried to do a research and learn more about it.

randBin(
meaning "random Binomial", generates a random integer between 0 and n from a Binomial distribution.

How to use the randBin command:

1. Press [MATH]
2. Scroll to the farthest right until you get to PRB and press enter.
   
3. Select and press [randBin(]
   
4. Enter the numbers using the formula below

randBin( n,p,# of simulations)
n = number of trials
p = probability of success


* the seed that is on rand affects the output of randBin(


Example:
Design an experiment to determine the probability of getting 50% correct answers on a 12 multiple choice questions quiz if you try to guess all the answers.

randBin( 12, 1/4, 5)

[ 2 1 4 1 2 ]
[ 1 5 1 2 1 ]
[ 4 2 2 5 0 ]
[ 2 4 3 4 5 ]
[ 3 3 1 4 2 ]

Answer : P ( 50% or over ) : 3\ 25= 12%



and that's what i understand about the randBin( command. Please feel free to correct any mistakes or add in some information(s) that is/are missing.




next up is ... Eugene.