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Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
The starting corner equals the product of its two nearest neighbors. For example, sin A = cos A ⋅ tan A {\displaystyle \sin A=\cos A\cdot \tan A} The sum of the squares of the two items at the top of a triangle equals the square of the item at the bottom.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
In economics, demand refers to the strength of one or many consumers' willingness to purchase a good or goods at a range of different prices. If, for example, a rise in income causes a consumer to be willing to purchase more of a good than before contingent on each possible price, economists say that the income rise has caused the consumer's ...
Antichristus, [1] a woodcut by Lucas Cranach the Elder of the pope using the temporal power to grant authority to a ruler contributing generously to the Catholic Church. Quid pro quo (Latin: "something for something" [2]) is a Latin phrase used in English to mean an exchange of goods or services, in which one transfer is contingent upon the other; "a favor for a favor".
Comparative advantage in an economic model is the advantage over others in producing a particular good.A good can be produced at a lower relative opportunity cost or autarky price, i.e. at a lower relative marginal cost prior to trade. [1]
The common law of business balance, often expressed as "you get what you pay for", is the principle that one cannot pay a little and get a lot. That is, paying a cheap price will not guarantee the buyer will receive a product of high quality value. In other words, a low price of a good may indicate that the producer compromised quality.
A friend to everyone is a friend to no one; A journey of a thousand miles begins with a single step; A little learning is a dangerous thing; A leopard cannot change its spots; A man can do what he wills but he cannot will what he wills; A mill cannot grind with the water that is past; A miss is as good as a mile; A new language is a new life ...