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The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse. The triangle shaded blue illustrates the identity 1 + cot 2 θ = csc 2 θ {\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta } , and the red triangle shows that tan 2 θ + 1 = sec 2 θ {\displaystyle \tan ^{2 ...
Reciprocal actions differ from altruistic actions in that reciprocal actions tend to follow from others' initial actions, or occur in anticipation of a reciprocal action, while altruism, an interest in the welfare of others over that of oneself, points to the unconditional act of social gift-giving without any hope or expectation of future ...
The rise of sociobiology was not well received by mainstream psychologists, and so reciprocal altruism was reinvented under the term "norm of reciprocity" in psychology. Study of the norm of reciprocity is arguably less scientifically advanced than that of reciprocal altruism, judging from the degree of research underneath the name "reciprocal ...
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
So for example, in the friendship context, reciprocation means to give or take mutually but not necessarily equally. Overall reciprocal balance is more important than strict equality at every moment. Friendship based on reciprocity means caring for each other, being responsive and supportive and in tune with each other.
However, this might appear to conflict logically with the common semantics for expressions such as sin 2 (x) (although only sin 2 x, without parentheses, is the really common use), which refer to numeric power rather than function composition, and therefore may result in confusion between notation for the reciprocal (multiplicative inverse) and ...
The identity involving the limiting difference between harmonic numbers at scaled indices and its relationship to the logarithmic function provides an intriguing example of how discrete sequences can asymptotically relate to continuous functions. This identity is expressed as [10]