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.

Law of Sines/Cosines

The law of sines and cosines are for me were surprisingly difficult to understand at first since I wasn't there for the teaching. However, once I went over the lecture online it was fairly simple. Law of sines is really just cross multiplying. The formula goes like this, (shown in image). You'd then plug in the degrees of the angle into the Sin A/B/C spot and then place that over the length to it's corresponding side. Law of cosines goes like this (shown in second image). This one is a bit more difficult hence the unsatisfied face at the bottom. But it literally is just plugging in the angle lengths and side lengths and then ultimately fulfilling he algebra. It looks difficult but really, it's not.

Verifying trig identities

Verifying trigonemetric identities is quite a complicated process. To start with, u need to combine like terms and trigonometric functions together. Then you need to put all trigonometric terms on one side of the equation. After this you need to apply a trigonometric identity if there is the need for one. Then you would factor if it needs to be factored. Isolate the trigonometric function to one side, and finally  solve for the variable. Within this we use algebra, trig functions, and a lot of simplifying. 

Examples V

Zeros of a function

What is a zero of a function? The best definition I can give you is that a zero of a function is a variable that makes the function equal to zero when it is plugged in. For example if you needed to find the zero of x +8= 0, the zero of the function would be -8. Because -8 +8 = 0. For equations like this, that involve addition or subtraction, the zero is usually the opposite number(the negative). When the function involves multiplication or division the zero itself is just zero. Zeros of the function are important because it shows us where on the x-axis the function intersects. 

Peace-wise functions

Peace wise functions use more then one equation per graph. We do his to find if the equation is continuous or discontinuous. If there's no holes or gaps or you can draw it with one line, then the functions are continuous. If not then the function are discontinuous. 

The greatest integer function so represented by an x between two double brackets. 

Looks a little something like this. Except for the fact that the lines normally go on and on. This is just a shortened version.  There isn't really a main reason for having these functions, but the main, probably only point is to find whether the graph is continuous or nah.

What I learned this week

Well, to be completely honest with you, most to almost all of the content I learned in our first full week of school was review for me. It was definitely good review though especially since my brain still thinks it's summer. This was also helpful because it went through the main points from last year that I needed to recall.  This week however I have learned that I shouldn't turn in projects late. (Like this one). And what limits are. 

All About Cory Masuda

My name is Cory, but my full name is Cory Micah Toshiyuki Masuda. I was born and raised in Pasadena for pretty much my whole life. 

I am a junior transfer from Pasadena high school which I honestly did not enjoy very much. Some people were nice, and fun to be around. But the teachers weren't very helpful and other students got annoying fast. 

I play basketball as an extra curricular activity as since I have played since I could run around. 

My family consists of my parents, my older sister Gabby, my younger sister Cherise, my little brother Garrett, and the littlest of them all, Kaiya. 

I enjoy watching movies, hanging out with friends, drinking a LOT of boba and coffee, and traveling with my family.