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…
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…
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,…
Derived demand for labor depends on the market value or product price of the good or service (McConnell, Brue, & Flynn, 2011). The demand for labor depends on productivity of the market value of goods produced (McConnell, Brue, & Flynn, 2011). The production of products is done by laborers, or the labor demand, and the derived demand is from the demanded product that is done by the same laborers. The concept helps determine the demand for the labor of specific goods, what is needed, how much is…
A++PAPER;http://www.homeworkproviders.com/shop/bus-640-week-5/ BUS 640 WEEK 5 BUS 640 WEEK 5, Week 5 DQ 1 Good Will in Price Bidding. Sometimes, a bidder on a work contract may bid lower than what would maximize his/her profit from the contract and the reason for that is to create goodwill (to increase expected future business from the buyer). How would you value the goodwill that is obtained in this way? DQ 2 New Product Introduction. Bayer Schering Pharma AG, Germany…
There are several ways that the long run differs from the short run in pure competition. First of all, pure competition is defined by involving a very large number of firms producing a standardized product, for example, corn, where each producer’s output is nearly identical to that of every other producer. Also, pure competition allows new firms to enter or exit the industry very easily. During the process of pure competition, the short run allows the industry to repose towards a specific…
C(Q1)=8(q1)2 → MC1=16q1 C(Q2)=10(q2) → MC2=10 P=(150-4q2)-4q1 → Using double slope rule find MR1 → P=(150-4q2)-8q1 P=(150-4q1)-4q2 → Using double slope rule find MR2 → P=(150-4q1)-8q2 Set MR=MC to find best response function for each firm Reaction 1: P=150- 8q1-4q2=16q1 q1=6.25-1/6q2 Reaction 2: P=150-4q1-8q2=10 q2= 17.5-1/2q1 B. Cournot Nash Equilibrium price =$72.72 Cournot Nash Equiiibrium quantity= 3.63+15.68 → 20.63 C(Q1)=8(q1)2 → AC1=8(q1)2/q1 → AC1=8q1 C(Q2)=10q2 → AC2=10…
the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to state their response, I questioned their thinking and reasoning behind it in the hopes that they would use their prior…