Introduction
Transitioning to the second semester I began a new subject exploring trigonometry called Measuring Your World. We went over tangent, arc sine, arc cosine, arc tangent, law of sines, and law of cosines. Learning a new subject is quite challenging and frustrating, you're bound to find bumps along the way and are expected to learn from them. Down bellow I will show you what I learned, but most importantly how I managed my challenges and how I learned from them.
Proving The Pythagorean Theorem

Our first assignment was called Proof By Rugs and what the problem asked was to see if Al and Betty's shaded rugs were equal and we were asked to solve that using the Pythagorean theorem . Just by observation you can see that both Al's and Betty's unshaped rug area's where the same so in conclusion they would have the same shaded area. Though, we had to prove that by using the Pythagorean theorem. At first I wasn't sure on what to do so I looked at the example of the Pythagorean theorem on the top of the paper which helped clear things up. Later I learned about distance formula which is used to calculate the distance between point A ( x 1 , y 1 ) and
B ( x 2 , y 2 ). To help remember and be less confused I compared it to the Pythagorean theorem because it was relatively the same thing. 
Using The Distance Formula and Finding Points on a Unit Circle

Later on, I was tasked to use the distance formula to figure out the equation of a circle centered at the origin of a Cartesian coordinate plane. After receiving the problem I wasn't worried about not being able to understand what the problem was asking me because I was beginning to understand the problems through the practice of the worksheets. All the time seeing a bunch of symbols and variables would frustrate me, but after reading it carefully it was simply just plugging in the information. I found out that the formula was x2 +y2=r2 so I plugged in the information and continued the following steps and found it satisfying to know what I was doing.

SOH CAH TOA 

When I started learning about sin, cos, and tan I had a lot of trouble understanding and I really didn't know what to do. So I did what I normally did when I had to independently study. I went on khan academy and watched some of the videos and worked on the problems it gave me. This was one of my proudest moments because this was where I learned the most on both understanding my work and overcoming challenges. After watching khan it was really easy. The hypotenuse was always the side opposite to the right triangle, the opposite is across the given angle, and the adjacent was next to the given angle. When finding the sides lengths of a triangle you would use SOH CAH TOA. SOH means sin is equal to opposite over hypotenuse , CAH means equal to adjacent over hypotenuse, and TOA means equal to opposite over adjacent. Using this I was able to find the missing side lengths to the Mount Everest worksheet:

The Importance of Learning Trigonometry
Learning about Sine, Cosine, Tangent, arc sine, arc cosine, arc tangent, law of sines, and law of cosines is absolutely essential for solving 2d shapes. I always like to think of formulas as a puzzle piece and with enough of them you can put it together and get a better understanding of what you are looking at.
Sine, Cosine, and Tangent
When looking for the side lengths of a 2D triangle a tool that helps is called SOH CAH TOA.
Examples
Sine is defined as the ratio of the opposite to the hypotenuse (SOH)
Therefore:
Therefore:
Arc Sine, Arc Cosine, Arc Tangent
Arc sine and arc cosine work along side SOH CAH TOA, arc sine and arc cosine are a mathematical tools to solve side ratios. In general, if you know the trig ratio of a 2d shape but not the angle, you can use the corresponding inverse trig function to find the angle. This is expressed mathematically in the statements below.
Law of Sines and Cosines
The law of sine and cosine is useful for finding a missing angle when given an angle and two sides, or for finding a missing side when given two angles and one side.
Example
Measure Your World Part 2
In this second part of the project we were assigned to choose an object and measure its volume and area. At the time I was quite hungry and the only thing on my mind was pizza, so the next thing you know I'm ordering Papa John's. To get my measurements I looked up the size of a large pizza and it was 14 inches and to double check I ordered in. I also needed the measurements of the box so ordering in was a good idea since they did not have the box measurements online and I did not want to make any assumptions.
With the info I needed I got to work which was simply plugging in the numbers. The formula for finding the area of a circle is A = 𝝅r² and with my measurements it equaled out to 615.75, and this is how I found my measurements for the box and the pizza.
With the info I needed I got to work which was simply plugging in the numbers. The formula for finding the area of a circle is A = 𝝅r² and with my measurements it equaled out to 615.75, and this is how I found my measurements for the box and the pizza.
Reflection
The challenges I faced in this project was the work load because I did not a partner so I did not have the aid of dividing my work, but I managed it by asking for help. A habit of a mathematician that I showed was persistence because there was a lot of times were I felt hopeless and wanted to give up but I kept going and asked for an extension when I needed it and was able to give my presentation. If I were to do things differently it would be working with a group because there are times were I can't do it all by myself.