Sharing Teaching Ideas: Discovering the Law of Sines

1991 ◽  
Vol 84 (8) ◽  
pp. 634-640
Keyword(s):  
The Law ◽  

Before my precalculus students derived the law of sines, I wanted them to explore the relationships between the angles and sides of a triangle. In particular, I wanted them to develop a conjecture about the proportionality between the sines of the angles of a triangle and the lengths of the sides opposite the angles. After they perceived a pattern in several triangles, my goal was to get them to predict the law of sines before moving to a formal proof.

1977 ◽  
Vol 24 (1) ◽  
pp. 83-84
Author(s):  
Theodore Lai

Bingo, like other games of chance, can be used in teaching ideas of probability. An introduction to probability may begin with simple experiments using the “law of equal ignorance,” which is the basis of the theory of probability. In a fair experiment, each possible outcome has the same chances to occur. That is each outcome is as “ignorant” as the other. In an unfair experiment, an outcome is favored to occur over the other possible outcomes; the favored outcome is not as “ignorant” as the other.


1989 ◽  
Vol 82 (2) ◽  
pp. 109-111

I have been teaching trigonometry for several years. One of my pedagogical concerns has been to be able to communicate more clearly the ambiguous case (SSA) in solving an oblique triangle by using the law of sines.


2002 ◽  
Vol 95 (2) ◽  
pp. 114-116
Author(s):  
Elizabeth P. Harrison

The laws of sines and cosines easily lend themselves to links with other areas of algebra and geometry. The most-used link is probably that of congruent triangles, but additional links exist with imaginary numbers, the quadratic formula, parabolas, zeros of functions, and the triangle inequality.


1868 ◽  
Vol 14 (67) ◽  
pp. 334-345 ◽  
Author(s):  
T. Laycock

That medico-mental science is often at variance with the doctrines and decisions of the courts of law is a fact too well known and too generally admitted to need formal proof. It is almost as generally assumed that the scandalous failures of justice, which too often result, must be attributed to the defective education and knowledge of the profession. It is alleged that, as a body, we are for the most part ignorant and theoretical in matters relating to insanity, and if not ignorant, then presuming, and often using the little knowledge we possess, rather with the intent to rescue thieves and murderers from the legal consequences of their crimes than to help the administration of justice. It is certainly a fact which many of us lament that the corporate bodies of the profession generally, including the general medical council, ignore the subject as a distinct department of medical education; and consequently medical practitioners, not being duly trained, do sometimes appear to great disadvantage in courts of law. Medical shortcomings are not, however, the subject of my paper, but certain fundamental defects in the principles and procedures of the law which render medico-mental science sometimes even worse than useless, and always less useful to the commonweal than it might be, if rightly adapted to the needs of modern society. Nor would it be difficult to show that some of the crime and folly which occupies our courts and fills our reformatories, prisons, workhouses, and lunatic asylums, is capable of prevention by a well-devised use of medico-mental science. As these matters are wholly beyond the powers of the profession, I shall ask leave to move at the close of the discussion that a committee be appointed, with power to take such steps as may be thought necessary to secure a thorough inquiry by the Government into the relations of medical science to the administration of the law in regard to all persons mentally disordered or defective, with a view to such improvements as may be practicable.


1998 ◽  
Vol 91 (4) ◽  
pp. 298-299
Author(s):  
Ingrid Novodvorsky

This project is one that I have been using for the past three years in my Advanced Placement physicscalculus and calculus classes. Before this project, I had introduced the power rule as a given fact and then demonstrated with graphs of monomials that the derivative is of one less power than the original function. I also used the formal proof involving the limit definition of the derivative. However, I sometimes felt that this method fell into the realm of “it should be intuitively obvious to even the most casual observer that …,” and my students never truly realized how the power rule for monomials elegantly expresses the concept that the derivative is the slope of a function.


2015 ◽  
Vol 20 (3) ◽  
pp. 72-84 ◽  
Author(s):  
Paula Leslie ◽  
Mary Casper

“My patient refuses thickened liquids, should I discharge them from my caseload?” A version of this question appears at least weekly on the American Speech-Language-Hearing Association's Community pages. People talk of respecting the patient's right to be non-compliant with speech-language pathology recommendations. We challenge use of the word “respect” and calling a patient “non-compliant” in the same sentence: does use of the latter term preclude the former? In this article we will share our reflections on why we are interested in these so called “ethical challenges” from a personal case level to what our professional duty requires of us. Our proposal is that the problems that we encounter are less to do with ethical or moral puzzles and usually due to inadequate communication. We will outline resources that clinicians may use to support their work from what seems to be a straightforward case to those that are mired in complexity. And we will tackle fears and facts regarding litigation and the law.


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