Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse functions of cosine, sine, and tangent. For the first inverse function, cosine, we know that it is obviously the inverse of cosine. The cosine function uses a angle of a right triangle and gives use the ratio of the x-value and the r-value (“Trig Functions:…
evolved from the original chord function to a plethora of functions and identities throughout the ages, many of the identities were already known in antiquity and utilized to measure distance and location in the skies. This paper provides a short review of the development of the sine and a short review of the development of the remaining trigonometric functions. The paper ends with an instructional suggestion to teach the fundamental and Pythagorean trigonometric identities using a diagram…
Here the teacher can remind or teach students that tangent lines touch circles at only one point. Once again the teacher can invoke prior knowledge by asking students what they know about the original triangle and the new triangle just drawn. When students respond they are similar triangles and the conversation develops to emphasize that similar triangles have proportional sides, the teacher can help students form a proportion with the ratio of sine and cosine equal to the ratio of tangent and…
Abstract: - Mathematics is a fascinating subject filled with concepts and ideas that have been formed and developed throughout time. This paper focuses on the contributions made by Islamic mathematician Muhammad Al-Khwarizmi to the difference subjects of algebra, geometry and trigonometry. Ideas discovered by Al-Khwarizmi are discussed as well as other concepts that serve as proof of his understanding of various complex ideas we use nowadays. These concepts include simplifying equations,…
Various types of knowledge are used for daily activities and do not always give us purpose and meaning. For example, in mathematics, the unit circle plays a key role in describing the graphs of the six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. Although memorizing and being able to cite the values of the each trigonometric function at each pi without a calculator is extremely useful and quite impressive, I find valuable information adds no personal purpose…
1. Henri Lebesgue [8] Lebesgue is credited for many amazing discoveries to different areas of mathematics. In the area of topology, Lebesgue is known for his covering theorem which is used for finding the dimensions of a set. He is also credited for his work on the Fourier series. He was able to demonstrate that using term by term integration of a series that were Lebesgue integrable functions was always valid and therefore, gave validation to Fourier’s proof of his series. What is now…
Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…
John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…
The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
the equation & based off what I did I'm assuming that his possible answer came out not to be an real answer to his problem & that is mainly because the equation itself is not true when eighty one is inserted for the letter x in the default problem. Okay so basically for this particular problem we have to think of f of x as basically the y value if that makes sense. So this would mean that if you use addition for the number two & + to the letter y we will see the function go up by two. The…