Repeating Decimals

Repeating decimals is a way to find out the decimal numbers that infinitely last like .3333... or .1515... To accomplish this, you use the formula, a1/1-d. a1 = the first decimal place it goes up to as a fraction, so for .3333 a1 would be 3/10 because it's .3 which is 30/100 or 3/10. then d = the difference between the first and next digit. Since .3333 repeats after every decimal, d would be 1/10 since it goes downward by 1/10 each digit. The answer would be found after you multiply the reciprical of the bottom to the fraction at the numerator and in this case it would result in 3/9.

Trig Review Week

Trigonometry to me is like a complex, aggravating, annoying, puzzle that takes constant 100% thinking to solve. In order to solve trig problems, you need to know each of the very many trig formulas. With these formulas, you attempt to algebraically solve each problem by using the trig formulas to cancel out or add onto each equation trying to make them equal. An example of a formula is sin^2 + cos^2 = 1. This is utilized frequently in order to make everything in an equation equal to sin or cos. 

2nd Semester Summary

This semester, I think I really I definitely improved as I focused on acheiving the goals I had set at the beginning of the semester. In the beginning I wanted to complete all hw, not fall asleep in class, and avoid careless errors on tests. Well to follow up on my goals, I completed most of my hw leaving behind approximately 2-3 assignments which is still an improvement compared to last semester. I also only fell asleep once in her class the whole semester, like this here is the true accomplishment since I barely get any sleep. And I also brought my average test grade up to around a B+. So overall I would definitely say I had a better semester then first semester. 

Here's an artsy pic I took a while ago :D

Polar Coordinates

Polar Coordinates are another way to graph dots like rectangular coordinates. The difference is that rectangular coordinates are plotted with x and y coordinates (x, y) while polar coordinates are done through r and beta (r, beta). Beta is represented with a symbol that looks like a zero with a horizontal line crossing the middle. r represents the circles that protrude outward while beta represents the position of the circle it is located. Each polar coordinate can be graphed in 4 different ways, (+, +), (-, +), (-, -), (+, -). To find r with rectangular coordinates, you use the formula r^2 = x^2 +y^2. This form of graph overall is almost equivalent to rectangular coordinates except the graph used for polar coordinates is circular. 

  

My Polar Equation picture

 

Parabolas

Parabolas are weird U shaped lines. They consist of the vertex, focus, directrix, and the axis of symmetry. The equation for a parabola that signifies it's a parabola is (h - x)^2 = (y -k). The x and y will switch depending on if the parabola is horizontal or vertical. The vertex is just the h and k values that would make each side equal to 0. The focus is (h, k+c), the directrix is k- c and the axis of symmetry is whatever x is. The c value comes from c^2 = a^2 - b^2. 

2nd semester goals

In the year of 2014 and the first semester of my junior year of high school, I feel that in my honors math

analysis class I achieved certain goals well. But i definitely need to improve upon a plethora of aspects that ultimately build up my overall grade. To start with, I personally believe I accomplished the hw to the best of my abilities. However on the other hand, I wasn't consistent within my accomplishment of fulfilling all my hw. Another good thing would be that I took thorough, specific notes on most of the lessons. Yet throughout these notes I fell asleep frequently due to lack of sleep the previous night. So acquire more sleep would be a reasonable goal. And finally, I feel for most tests, I was able to remember the material to the best of my understanding. But on these tests, I made careless errors and for some I didn't know the material since I was sick/absent constantly throughout the year. Mainly I need to work on my attendance. 

Off topic my favorite Christmas story over break would be celebrating with friends and family while my favorite traditional Christmas story is the Christmas Shoes.

Here's my family on New Years😋