Polar coordinates

Polar coordinated are coordinates plotted on a circle graph. The circle graph is basically an extension of the unit circle. Since it is an extension of a unit circle, there are two kinds of points that one can plot: rectangular and polar. The rectangular coordinate points are the basic (x,y) coordinate pair where x=rcos(theta) and y=rsin(theta). The second is the polar coordinate which is represented by the coordinate pair (r,theta) where r2=x2+y2 and theta is equal to the inverse tangent of theta. There are four ways in which a polar coordinate pair can be written: (+,+)(+,-)(-+)(-,-). To plot polar coordinates. On has to find the value of theta on the unit circle then either r circles out wards or r circles towards and last the origin in the opposite way if it is negative. 

Second Semester Summary

Second semester was a little better than first semester in terms of being organized, but that quickly failed and I regressed to my original slob form. There is only two weeks of school left and I am determined to get them over with as soon as possible because I am so done with school. I have three binders that I carry around me now and days because I stuff papers and such into random binders and so I have to carry them all just in case I need one specific worksheet I need to turn in. Math wise, I am not very happy with myself in how I did second semester. I began a lot better than first, but my test scores were constantly low and blogs were forgotten about constantly as well. These two things are going to take a huge toll on my grade and that is one thing that I am very scared of. In terms of my other classes like I'm just done.

Trig Review Week

The presentations that my classmates gave were extremely helpful in remembering certain topics and methods of solving a problem. Many of the concepts I had forgotten that we had even learned therefore it was really nice to be able to refresh my memory in such a small amount of time. I think the actual trig itself is the hardest since there are so many of the identities to memorize and I get overwhelmed. I need to review a lot for the final since many of the topics that we talking about during the presentations were somewhat difficult for me as well as the induction/deduction arguments.

Repeating Decimals

Every repeating decimal is the sum of an infinite geometric series. In order to find the quotient of integers (the fraction) of a repeating decimal, first, the decimal has to be written as a quotient of integers and the geometric series has to be seen. From the broken up decimals, the sum should be really easy to find. After finding the sum, the corresponding parts of the equation S=a/1-r. The final answer should always be checked by a calculator just in case.

Parametric Equations

In parametric equations, first, a t/x/y has to be made in order to be able to graph the equation. The graph should have arrows pointing in the direction the line is going. After sketching a graph, one has to eliminate the parameter using algebra and trig identities in order to solve a equation. The parameter can be eliminated through substation or elimination, so long as the final answer is a rectangular equation.

Partial Fractions

Partial fractions are basically the reverse of multiplying two factors out into one. Given a linear equation, the denominator has to be factored out into its two (or more) factors. Above every factor should be a letter so the set up looks something like A/(x-2) + B/(x+3). However, if one has a denominator that cannot be factored, a quadratic equation, then the numerator becomes Ax+B (and the variation of this set up). If the denominator is squared at one point, when factoring this out, this one equation that is squared has to create two different partial fractions. One must be the factor in the parenthesis and the other is the whole factor (A/x+B)^2 + B/x+B.

Power of Hanoi Mathematical Induction

Tower of Hanoi is a game in which there are disks of different sizes stacked onto of eachtoher in decreasing order "( smallest on top and largest on the bottom) and the whle point of the game s to move the disks across to another empty disk holder in the least amount of moves. For the power of hanoi, the mathematical induction began with 2^n, the number of moves it took to the initial tester to get the equation 2^n-1. This is then proven by plugging the variables into the induction equations and then solving to ring true.