Trigonometry is the study of triangles and the relationship of angles and sides in a triangle. Before even finding side lengths using trig, you need to label all the sides of the triangle. There are three special names for each side; there is hypotenuse, opposite, and the adjacent. The hypotenuse is the longest side and is always across from the right angle (90-degree angle). The opposite side is across from the reference angle. And the adjacent is the side beside the reference angle.

What are the ratios?

SINE RATIO = opposite (divide by) hypotenuse

COSINE RATIO = adjacent (divide by) hypotenuse

TANGENT RATIO = opposite (divide by) adjacent

An easy way to memorize these ratios is with the acronym SOH CAH TOA. Therefore is each of the ratios first letters into a big word.

For every trig equation : Ratio (REFERENCE ANGLE) = side 1/side 2

In this example, we need to see what ratio we will use, and from the process of elimination the ratio needed is SINE. Next, we use algebra to find the answer.

When simplifying an expression that includes exponents there are exponents laws that one could use to answer the question easier. The laws of exponents can be thought of just “tricks” or shortcuts that help us work with exponents in equations. Some of these laws for exponents are the Power Law, Multiplication Law, and Division Law. However, we are going to focus on just the division law.

The first thing to do when using the division law is to identify the same bases with exponents. If the bases are not the same, you can’t use the division law and won’t be able to simplify it any more. Next, you will subtract the exponents leaving you with one number with one exponent. To divide exponents (or powers) with the same base, subtract the exponents. The coefficients (if any) won’t be affected by the division law. As division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

My example:

If when you are subtracting the exponents and the result is a negative exponent then you will use the Negative law to further simplify the expression.

I choose to get my data from the site, https://ourworldindata.org/forests and took the topic deforestation over the years. From my data visualization, I decided only to take the data for the temperate forests to simplify to the infographic, that I was going to make. The reasoning behind creating this data visualization in the way I did was to ultimately simplify the information and choose only one set of the data provided. I also wanted to include some art into the infograph as I enjoy to draw and be creative. I believe that when the reader is looking a the poster, they would clearly see the drastic decrease of forest throughout the years.

This week when I was doing a practice question to find the least common multiples when using numbers’ prime factorizations. I could not figure out why I kept on receiving with the wrong answer, no matter what. What I was doing wrong? I tried doing it over again but came up with the same results. Then after more explanation, I learned that I multiplied the common numbers of the prime factorization twice instead of the once I needed to do. I also now have a useful technique to find the least common multiples.

Firstly, what are the least common multiples? Least common multiples (LCM) are the smallest positive number that can be divisible by both of the numbers. The way to determine the LCM is to take all the prime numbers of one of the numbers and multiply by any additional factors in the other numbers. An easy way to find the common numbers in two prime factorizations for the LCM is to use a Venn diagram. You can take a Venn diagram and put the common numbers from both of the prime factorizations in the middle. After that, put the remaining numbers from their prime factorizations in the other two sides of the Venn diagram. Then multiply all the numbers together for the LCM.

Reflection : The type of writing that a synthesis essay uses is very hard to do right, however I am proud on how I was able to write formal properly by not using you, I, or us. So one thing, I did well on my essay was the langugue I was using to compose my essay. Another thing that I think that I did really well was intro as the hook sentence was quite catch. A big thing I want to improve on is being able to write in block style and finding out the proper formatting. Also, when I first gave in my essay I forgot to write a title, so for next time to read from start to end of my essay before
handing it in.

Fog blocking and hazing over the happenings on the outside,
we are barricaded and blind from being in our own higher worlds,
with no ways for us to hear pass the harsh winds,
that are quickly chewing them apart,
They are stuck in what is bubble gum, unable to imagine a future
as this is the place where we need to restart.

We are trapped in our self-made glass bubbles,
Safe, are we?
Yes, but with us being oblivious when having our heads curled to the ground,
The fact is that these bubbles are keeping us spellbound,
From realizing this organized chaos.
Chaos of people treating their fellows in such an inhumane way,
This treatment has had its overstay

In the naked light, we can see ten thousand people, maybe more
Drained to the core by this war of oppression, we had ignored
For way too long, its crazy how much we are in the wrong,
Still we are hypnotized by this cheery and strong birdsong,
We sing together to belong,
This is the future, let’s come along,
Please…unfreeze and break from our individual glass bubble
And escape these horrible toxins and overcome the rubble.

Mackenzie Clarke’s “Self-Made Bubbles is a free verse poem that touches on the theme of how there is oppression that still happening in this current age, but our society chooses to have a blind eye to this fact and ignore it when they see it. Her poem explores and goes into the inquiry question of “What motivates us in the face of despair and oppression?” but when addressing we could have the motivation but not also the drive or want to fix the problems of our society. The phrase, “This treatment has had its overstay” is an example of personification where she expresses her belief that we need to find the will to change and stop the oppression from happening. The use of the allusion “unable to imagine a future” hints on how it is hard for the people who are being oppressed to think or have the hope that a time where they won’t be a target of oppression. The symbolic title of “Self-Made Bubbles” shows that it not only society shielding us from the seeing information, however, we also put up figurative walls to be oblivious a not see the full story of what is happening. There is a line in the poem talking about a hypnotizing birdsong, this part contradicts as birdsongs are usually perceived as cheerful and happy things. However, the author is referring to how society sometimes masks the bad with a distraction and if we try to look pass it, it is going against the norm or society.