Trig Review Week

During this week, we decided to review trigonometry. 

We looked at trying to simplify trigonometry functions and then we looked at verifying. After that we looked at solving trigonometry and looking at the trig identities. All of these identities help us solve, verify and anything dealing with trig.

Trigonometry will be in the final and we reviewed these to understand trig as it was a bit of a struggle for some of us.

This was one of the things we looked at as we reviewed.

SEE YOU NEXT WEEK!!!

Week 16: Repeating Decimals

Repeating decimals is pretty simple to understand.
Every repeating decimal is the sum of an infinite geometric series.
so what you do is write the decimal as a quotient of fraction intergers
so if it was .3333333
it would be 1/3

So the steps are
1. write as a geometric series
2. find the sum with asub1/1-r r is what you multiple by.

Above are two examples adn how you solve it. 

you turn it into a fraction and it would be growing in the denominator and then you find out what r is and then you plug it into the sum equation to find out what the sum would be. then you find what the sum would be in fraction form.

SImple enough.

Hope you understand.

SEE YOU NEXT TIME!

Week 15: Parametric Equations

Parametric equations are equations that you make and understanding the direction of the shape being created.

Step 1: Sketch a graph or to be more exact make a table
Step 2: Eliminate the parameter by elimination/substitution and trig identities
Always solve for y

It is quite simple and usually you will get an equation like
x=t^2
y=t^3
above is the parametric equations
then you will receive a parameter ’t’
-1≤t≤2
then draw the table. it is presented below. You put in the given numbers into t and find x and y. Then you graph it and put arrows in the direction you travel and make a line.

after that you try to eliminate t by using substition and solve for y
if there is trig you use the trig identitites while without trig you just use eilmination and substitution.
Below is an example with trig. You do the same exact thing but you use trig and solve for y and you cannot have trig in the end.

That is how you use parametric equations

SEE YOU NEXT WEEK!!!

Week 14: Partial Fractions Composition

We finally finished the book for Pre-Calculas and we decided to look at old information that we decided to skip over. One of the few things that we did was Partial Fraction Decomposition. Partial Fraction Decomposition is when you take an answer that is completely answered and turn it back to what it looked like before.

like if the answer for a question was:

1/x+1 +2/x+3

it would go to 

(3x+5)

(x+1)(x+3)

To do this there are about four steps to set it up

1. Divide if improper

2. Factor Denominator

3. Linear

4. Quadratic

Also how do you solve it.

1. Multiply by LCD

2. Group terms by powers of x

3. Equate coefficients

4. Solve the system of equations

Now there are 4 cases.

the first case is when the system is just a binomial : x+1 or x-1 or etc.

So below is one example of case 1

You first try to factor it and then you put it as A and B.

After that you then make it so you find it as a common denominator

Then you use A and B and group it together with x^2 and x and regular numbers. then solve the system of equations at the end.

The second case involves bx+c which is only used when there is a square or exponent inside the paranthesis. You solve the same way and you keep going.

The Third case is when there is a square on the outside. You make it so first there is the first without the square and the second one with a square. Then you continue on.

The last case deals with long division. You only do this when the exponent is bigger on the top than the bottom. THen you continue to solve all the way through.

That is how you use partial fraction decomposition
SEE YOU NEXT WEEK!!!