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😋

Chapter 4 Summary

In chapter 4 we learned all about sins, cosines, tangents, and all other types of trigonometric functions.  We learned the acronym SOH-CAH-TOA and when to apply it to our work. We also learned about sum and difference formulas, double angle formulas, half angle formulas, and Pythagorean identities. And finally we were introduced to the usages of Pythagorean functions. This chapter was actually a lot more harder as it required full attention to detail within working out the problems. I have ran out of ideas for a photo so here's a really cute dog I found on the internet. 

Chapter 3 summary

In chapter 3, we learned about functions. To be specific: polynomial functions, zeros of a function, and rational functions. We learned about polynomial functions and how to divide them both the standard way and through synthetic division. We also learned about the process of finding the zero of a function. And finally, we learned about about the vertical and horizontal ampsymtotes of graphs. Overall a simple chapter when effort is put into it.

Example of zero of function

Mr. Unit circle

Mr. Unit circle is quite the handy device. It displays the four quadrants on a standard graph which already is a big help. Along with that it shows the measurements of the graph in degrees and radians. And with that it displays the sins and cosines with the standard right triangle lengths. The standard right triangles are of the following: 30-60-90 right triangles and 45-45-90 right triangles. 30-60-90 triangle have lengths of 1, sqr root of 3, and 2 and 45-45-90 triangles have lengths of 1, sqr root of 2, and another sqr root of 2.

Tangent

Tangents are fairly similar to sines and cosines. The rules of tangent are stated in the third part of the SOH-CAH-TOA acronym. What It means is that, Tangent is the Opposite side length of the specific angle divided by Adjacent side length. Along with the sine and Cosine functions, tangents are trigonometric functions used to find the missing side lengths and angle lengths within a triangle. Personally tangent functions are more difficult then sine and Cosine 

Sines and Cosines

Sines and Cosines can be described simply with the acronym SOH-CAH-TOA. This means that the Sine of an angle within a triangle is the Opposite side length divided by the Hypotenuse of the triangle. For Cosine it means the Adjacent side of the angle divided by the Hypotenuse. Sines and cosines are used as trigonometric functions to display a ratio of the side lengths. One usage of these are for the discovering of certain unknown side lengths or angle lengths. With the use of a unit circle it is easy to see the sines and cosines of different triangle length. Unit circle is shown in image

What a function is

What is a function you ask??? A function is a mathematical equation that represents steps you follow to bring together a sequence or graphed line. For example, (look at picture). This function states that y equals double the x variable plus 3. The graphed line represents the numbers that would correspond to this function. Meaning that when you want to fight the y variable with any x variable, you go along the line made to where the x and y variables would meet.