Search results
Results from the WOW.Com Content Network
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.
Identity 1: + = The following two results follow from this and the ratio identities. To obtain the first, divide both sides of + = by ; for the second, divide by .
As an alternative to using the identity for the sum or difference of two sines, one may cite the trigonometric identity tan 1 2 ( α ± β ) = sin α ± sin β cos α + cos β {\displaystyle \tan {\tfrac {1}{2}}(\alpha \pm \beta )={\frac {\sin \alpha \pm \sin \beta }{\cos \alpha +\cos \beta }}}
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
Lambek's correspondence is a correspondence of equational theories, abstracting away from dynamics of computation such as beta reduction and term normalization, and is not the expression of a syntactic identity of structures as it is the case for each of Curry's and Howard's correspondences: i.e. the structure of a well-defined morphism in a ...
In the above identity, α, β, δ line up throughout and γ occurs twice in one term due to a contraction (once as an upper index and once as a lower index), and thus it is a valid expression. In the invalid expression, while β lines up, α and δ do not, and γ appears twice in one term (contraction) and once in another term, which is ...
Alpha is a way to measure excess return, while beta is used to measure the volatility, or risk, of an asset. Beta might also be referred to as the return you can earn by passively owning the market.
Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that