Trigonometry

So many people have different interpretations of mathematics, in elementary school we learn that if you have 5 apples and your neighbor takes 3 away you are only left with 2. In middle school we were shown that there are 360 degrees in a circle and a numerous variety of rules and theorems that seemed only relevant for that section. We learned about sine, cosine, and tangent, which were chiseled in our brain. In high school we were introduced to things I didn’t know existed, such as derivatives,…

THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…

Equation of trendline 1 calculation: m= rise/run = 12/15 = 0.8 c= 5.9 y= 0.8x + 5.9 Equation of trendline 2 calculation: m= rise/run = 25/45 = 0.5 c= 17.6 y= 0.5x +17.6 Point of intersection: Equate both trendlines to find point of intersection 0.8x + 5.9 = 0.5x + 17.6 x= 39 Since x=39, x2= 9 as x2 represents x in descending order. R2: R2 for trendline 1 = 0.98 Correlation coefficient for trendline 1= 0.96 R2 for trendline 2 = 0.98 Correlation coefficient for trendline 2= -0.99 Ratio…

contexts in order to prepare them to use mathematics beyond the classroom: throwing “basketball” paper wads to determine the best mathematical model, performing “Function Aerobics” as the graphs shift, and measuring football lights outside using trigonometry. In “Geometry Store Geometry”, my students explored the surface area and volume of various food items. Using this knowledge, students designed packages to maximize profit while at the same time reducing cost. By building projects,…

After processing the data to find the mass of sodium bicarbonate as well as calculating the percent errors, standard deviation and etcetera, many trends and discussion topics arose and the data produced had small calculations. The percent error showed scattered results. When looking at the table, the percent errors can go from 7.05% to 200% and the reason for the extremely high percents were systematic errors made while measuring vinegar or other measurements. Two of the three deformities in…

his book Canon Mathematicus in 1579. The book contained a collection of trigonometric formulas and tables. Viete was also responsible for trisecting an angle and the construction of the regular pentagon. Bartholomeo Pitiscus had coined the term trigonometry in the title of his 1595 book, Trigonometria. This book was split into five parts on spherical and plane geometry. In 1609, a mathematician named Johann Kepler achieved the first major accomplishment of the century. Using planetary…

there is a group that can only be described as teachers who hate teaching. Instead of making you feel excited about the subject, they make you dread it. They overload you with busy work, or complain about how we act. They insist on how we will use trigonometry in our everyday lives, and how this information is needed to be successful. Ideas of high GPA and test scores are pounded into our heads. If you don’t make high grades,…

The limitations of calculating π included the tools given for calculation. A paper tape measure consisted on units of centimeters and approximation to the nearest tenth could have limited the exercise. The best method was picking the closest centimeter measurement visibly possible for the diameter and circumference by wrapping the paper tape measure around the circles. The worst method would be using a ruler or meter stick. The only improvements that could be made is the use of smaller units to…

because I was placed in Math 330 Trigonometry and I feel that my skills were not truly tested. I believe I should be placed into Math 370 Precalculus. I wish to challenge the prerequisite of Math 330 Trigonometry and assume the responsibility to succeed in Math 370 precalculus despite not meeting the prerequisites. Completion of Math 330 requires student to be able to find degree and radian measurements of angles, right triangle trigonometry, unit circle trigonometry, graphs of trigonometric…

The lattice symmetry of quartz α-FePO4 is trigonal. Its space group is P3121. The lattice symmetry of quartz β-FePO4 is hexagonal. It space group is P6422. According to the article, only two of the various quartz homeotypes which exhibit alpha-beta transitions have been studied in detail at high temperature. One of them is Silicon Dioxide. As such, it is possible for silicon dioxide to have the same structure when the chemistry is completely different. Since iron…