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Pythagorean identities. Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
Euler's formula states that, for any real number x, one has = + , where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively.
Conventionally, an abbreviation of each trigonometric function's name is used as its symbol in formulas. Today, the most common versions of these abbreviations are "sin" for sine, "cos" for cosine, "tan" or "tg" for tangent, "sec" for secant, "csc" or "cosec" for
In computing, they are typically abbreviated to sin and cos. Some CPU architectures have a built-in instruction for sine, including the Intel x87 FPUs since the 80387. In programming languages, sin and cos are typically either a built-in function or found
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.
Japan is a constitutional monarchy with a bicameral legislature, the National Diet. A great power and the only Asian member of the G7, Japan has constitutionally renounced its right to declare war, but maintains one of the world's strongest militaries.
PPP largely removes the exchange rate problem but not others; it does not reflect the value of economic output in international trade, and it also requires more estimation than GDP per capita. On the whole, PPP per capita figures are more narrowly spread than nominal GDP per capita figures.
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