We learned how to transform trig. Functions through using expressions. This allowed us to transform expressions to the “desired” form. This required us to be able to visualize sections and see how transformations are possible. We started this by learning about the 3 different properties that we could use to transform. The reciprocal property has three expressions: sec(x)=1/cos(x), cot(x)=1/tan(x), and csc(x)=1/sin (x). Three Pythagorean properties: cos^2(x)+sin^2(x)=1, 1+tan^2(x)=sec^2(x), cot^2(x)+1=csc^2(x). As well as, two quotient properties; tan(x)=(sin(x))/ (cos(x)), cot(x)=(csc(x))/ (sec(x)). Once we learned the properties we started to learn how to transform the properties. To start off you rewrite the expressions, picking the “easier” side to start off with. Next, you look for algebraic thing to do. Following you multiply the clever form of 1. Third, look for trigonometric things to do. Lastly, keep looking at the result and thinking of ways to get closer to the answer. During this unit I think I had to spend the most time on trying to play catch up and get a solid understanding of transformations before moving on to the concepts that build off of transformations.
The chapter 7 quiz fits into the story as, this was one of the days where the day before I was absent and then came back and asked questions before class. More specifically I came in that day and asked questions before the quiz, trying to understand the concepts before I took the quiz. The classroom content that is visible in my chapter 7 quiz is using the properties listed above in used in transformations. So, like “Prove algebraically that (1+cos(x)) (1-cos(x))=sin^2”. In this problem you first start with the more complicated side (the one with cos). From there you would complete the multiplication=1-cos^2(x). You then use the Pythagorean Property cos^2(x) +sin^2=1. This means that if you flip it, 1-cos^2(x)=sin^2. The chapter 7 group quiz fits into the story of my learning process as it shows my growth in the concepts such as transformations and “learning opportunities”. Since we did not have a test without using groups, single growth is kind of hard to demonstrate. But overall I can say that for my growth, I learned in being better at understanding transformations and the perks that come with each. Some of the classroom content that is visible in this work, specifically, is the “learning opportunities”. In this group test we were faced with a specific challenge of learning a concept/section. This concept was the composite of a function and its inverse function. The equations used for this concept is f (f^ (-1) (x))=x and f^-1(f(x))=x. This means that provided x is in the range of the outside functions and in the domain of the inside function, it will work. Using this concept, this is why we get “saw-toothed” graphs, basically the graph can only hit to -1 and 1, so it is restricted.
In this project I had a lot of trouble at first understanding how to transform expressions. Through this chapter I got better at intuitively understanding when a transformation is necessary. I overcame this by continually doing problems and going through them. This meant that when or if I am having problems, I could talk to other students and work through whatever issue I was having. During this unit I think I had to spend the most time on trying to play catch up and get a solid understanding of transformations before moving on to the concepts that build off of transformations.
