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.