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…
Francisco Gutierrez 03.03 Linear Functions 1. The equation we have is 2x+3y=1200. The first thing you would need to do in the equation is subtract 2x to both sides. 2x cancels out and now we subtract 2x and 1200. You would end up getting 3y=2x-1200. Then finally, you would have to divide everything by -3. Your final answer for this question is y=-2/3x+400. Your slope is -2/3 and your y-intercept is 400. 2. So we know that our slope is -2/3 and the y-intercept is 400. You have one point on the…
New Balance is moving into a toning market with a pair of attractive shoes that has hidden balance technology. The purpose is to present, “Why walk when you can tone your body”, when you’re simply just walking or even doing your everyday chores. True Balance shoes promises 29% muscle activation and 10% calorie burn. Many women are getting intrigued with the idea of losing weight by these shoes from the percentages, but what if they percentages were lower. Would you still buy them? Even though,…
The Result With full data sheet of Rampo Valley Reservation park and Harriman State Park, we determine the relative density, frequency, relative frequency, relative dominance and important value. <Table 1> is Ramapo Valley Reservation Park’s table . <Table 2> is Harriman State Park’s table. Relative density is percentage of number of individual of one species by sum of the individuals of all species. Relative frequency is percentage of frequency by sum of the frequencies of all…
To ensure an athlete may return to play as soon as possible, a variety of rehabilitation processes should be implemented. These should include progressive mobilisation, graduated exercise (including stretching, conditioning and total body fitness), training and the use of hot and cold applicants. When each step is correctly addressed, it will increase the likelihood of a speedy reintroduction to sport. Progressive mobilisation is necessary to enhance the range of movement available. A…