Week 4 – Math 10 – Bearings and Angles of Elevations/Depression

It can be hard to solve problems using trigonometry if we don’t have a diagram to compare and look at. So when working to solve word problems knowing what bearings, the angle of elevation, and the angle of depression are helpful to create an illustration that will aid in the solving process.

What are bearings?

A bearing is an angle that is measured clockwise from the North direction. Planes and buses use bearings to determine a direction of travel based on their compass (as South from due North).

When solving many word problems, the angle of elevation or depression is determined by the eye level of the person and not from the ground. This is the line of sight, a sight line from the observer to some point of interest. To know what these angle mean, you also need to know what is something when it is vertical or horizontal.

Horizontal: is going side-to-side, for example, the horizon, a shadow, the ground

Vertical: is an up-down direction or position, for example upright, someone’s height, a tree, a building

The angle of elevation if the angle goes “upwards” from the line of sight. Therefore, the angle of depression is the “downwards” angle from the horizotal to a line of sight from the observer to some point of interest.

Week 3 – Math 10 – Finding Side Lengths Using Trig

What is trigonometry (trig)?

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.

Week 2 – Math 10 – Division Law

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.

Data Visualization – Deforestation

Even though, most people have a general idea that with the current years our forests are in danger. However, I believe that we don’t understand the drastic effects are happening. This leads me to choosing my data about the topic of deforestation over the years. After looking at some different sites the OurWorlinData was very helpful to gather my information (this is the site’s hyperlink: https://ourworldindata.org/forests)

My Raw Data:

In the raw data, there were two types of forest tropical forests and temperate forest shown. However, I decided only to take the data for the temperate forests to simplify to the infographic. My main reasoning behind creating this data visualization in an infographic way was to ultimately simplify the information and choose only one set of the data provided. I also wanted to include some art into the infographics as I enjoy to draw and be creative. Also, younger people tend to be able to understand info if there are pictures included (such as little kids with picture books). Another reason that the scale is made in a picture. I believe that when the reader is looking a the poster, they would clearly see the drastic decrease of forest throughout the years.

After I had finished the infographic, I wanted to add something else to add to the point on how important it is to see the huge difference in our forests. I was shocked by the facts on deforestation and then I decided to write them in the extra space.

My Data Visualization :

My Self Reflection :

Week 1 – Math 10 – Least Common Multiples

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.

Let’s do exemple:

Sterotypes can Destroy Lives

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.

Essay – TKAM -191pnya