• Why are there asymptotes in the graph of tangent?
    Why does it look the way it does?
    What differs in the graph of cotangent?
    Why do they look like giant "U's"?
    Why are there asymptotes in csc and sec?
    How do they relate to the graphs of sine and cosine?
  • There are asymptotes in the graph of tangent because you're dividing by  zero. It looks the way it looks because of the asymptotes and it having a relationship with the sin(x) (I HAVE NO CLUE!!!!!). The graph of cotangent will be shifted and flipped compared to the graph of tangent. They look like giant U's because they interlap each other forming U's. CSC and SEC have asymptotes because at every integer of pi like (pi, 2pi, 3pi...) it causes the equation of csc and sec to divide by zero. This creates an asymptote. They relate to the graphs of sine and cosine because have the same intersects. So sine has the same intersecting point at y=1 as csc. Same for cosine and sec.
 

College Loans...

I really don't know squat about college loans, but I did the research and had some help from my people. Here's my attempt at the problem.

Direct Subsidezed Loans - Loans that are available to undergraduate students. The U.S. Department of Education pays the interest on this loan. Students MUST have a fianacial need for the loan.
Direct Unsubsidized Loans - Loans that are available to graduate and undergraduate students. The students don't to demonstrate need for financial aid but they are responsible for paying the interest on the loan. The school determines the amount you can borrow.
Bank Loans - Private loans given out to students by an individual bank.
Interest Rates - Calculated by figuring out the number of days since your last payment and the interest rate factor.

I used an online calculator and found out if I pay $95.77 a month, I should be able to pay it off in about 4 years and 5 months. I don't know if this is right, but I tried...
 

Finding Real and Imaginary Zeros

During the test, I was freaking out because I wasn't sure what imaginary zeros were. I didn't know how to find them and I was running out of time. So I just went to the graphing calculator, plugged in the equation into the (Y= Function) and listed the zeros I saw. But now that I've watched the Finding Zeros Video, I know that you must graph the equation first to find all of the easy zeros. Next you'd find out how many zeros are accually in the problem. Then do synthetic divison using the easy zeros you found. What's left of the remainder should be the rest of you zeros (imaginary or real). I just found everything in the video.

Stating the Multiplicity

By the time I got to this problem (#12) that I put off because I didn't know how to do it, I had ran out of time. That's why I left it blank... But now I realize that this wasn't a hard problem.

Simplifying Imaginary Numbers

What I learned about simplifying imaginary numbers is that (i) with an exponent resets after (i)^4. I basically explained that in my work on the page. 
 
math_graph.docx
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September 09th, 2013

part_5_math_graph.docx
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    I'm not sure what I was going for when I made this. I had decided to put a bunch of circles inside of each other and make it look like a bullseye target board (thing); I don't know. I made each of the circles grow everytime by writting the equation x^2 + y^2 = 1, 5, 10, 15... and so on. I added a sine function just because I wanted to. Then I added two cosine functions that interlaped each other with the altitudes being 0.5. At that point, the two cosine function made my graph start to look like an eye, so I added the parent absolute value function to make the eye into an angry eye.

October 11th, 2013

Here that basketball problem that we had to do. The bank is open as Gavin would say, but I don't think it goes in... Sorry.
the_bank_is_open.docx
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