Tutor profile: Charles M.
What is the unit circle and why should I care?
The unit circle is a demonstration of the fundamental relationships between various right triangles and the relation of their internal angles to the ratio of their sides. It is also important for an intuitive understanding of sinusoidal curves and why they behave in their specific ways. Essentially, the unit circle is a circle of radius 1 unit, centered on the coordinates (0,0). All trigonometric functions default to the unit circle. For example, the expression cos(30) is answering the question "Given a right triangle constructed inside the unit circle such that the hypotenuse of the triangle is on the perimeter of the circle and the angle adjacent to the center of the circle is 30 degrees, what is value of the length of the adjacent short side divided by the length of the hypotenuse?" All trigonometric functions are answers to similar questions about the unit circle. Thus, understanding the unit circle will deepen your understanding of trigonometry as a whole. As for why one would care, trigonometry shows up in all sorts of interesting places. Sound and light waves are described by sinusoidal functions. More practically, your microwave is dependent on knowledge of these waves, and knowing how sinusoidal curves physically interfere helps build a microwave that heats food more evenly. Trigonometry helps engineers bank roads properly, so that the angle of the asphalt helps cars stay more stable at high speeds. There are many reasons to care about trig, and the unit circle helps you understand it just that little bit easier
What are the components of a good introduction?
The three major components of an introduction are the hook, structural declaration, and the thesis statement. The hook should be your first sentence, and should introduce the topics you intend to cover in relatively broad strokes. The tone should generally be inquisitive, and intended to provoke the curiosity of the reader. Next is the structural declaration. Here is where the topics you intend to write about in subsequent paragraphs are introduced in some detail. Finally, you unveil your thesis statement, which is a declaration of what you intend your paper to prove to the reader, the essential crux of the argument you are intending to demonstrate. An example introductory paragraph could read as follows: The five paragraph essay is a staple of high school writing, but very few people care to examine why that is so. I believe that this style of writing has become more and more commonplace due to three benefits foundational to the five paragraph style. First, formulaic papers are easy to grade objectively. The structure inherently provides metrics for teachers to quantify the ability of the student and make sure that they check all the boxes of a "proper paragraph" or "proper essay". Second, it provides a framework for students to develop ideas around. Having an inherent structure allows more inexperienced writers to focus solely on the content they want to prove and support, rather than the more abstract and difficult techniques around paragraphing and presentation. Third, it forces the writer to have enough comprehension of the material to come up with three distinct yet related pieces of their argument, which increases the likelihood that the student must actually read the material in order to write a coherent essay on the topic. These merits together make the five paragraph essay valuable to teachers everywhere and guarantee that this format is going to stay relevant for many years to come.
Subject: Basic Chemistry
How do ionic bonds form?
Ionic bonds occur when there is a large differential in the electronegativity of two molecules. More practically, this means that ionic bonds are most common between elements with valence shells that are almost empty and those that have valence shells that are almost full. For example, a salt like NaCl (common table salt) is a common ionic bond. Sodium (Na) is an alkali metal, and thus wants to give up its electron to form a more stable configuration. Chlorine (Cl), as a halogen, has the opposite intent, as it is most stable with an extra electron. Thus, when the two molecules interact, Cl takes the valence electron away from Na. This leaves Na at a net positive charge, and Cl at a net negative charge, and thus the two are attracted to each other by their opposing charges.
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