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The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [ 1][ 2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial ...
API gravity values of most petroleum liquids fall between 10 and 70 degrees. In 1916, the U.S. National Bureau of Standards accepted the Baumé scale , which had been developed in France in 1768, as the U.S. standard for measuring the specific gravity of liquids less dense than water .
For example, in a footnote, Thomson derived the value of −273 °C for absolute zero by calculating the negative reciprocal of 0.00366—the coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point. [15] This derived value agrees with the currently accepted value of −273.15 °C, allowing for the precision ...
List of refractive indices. Refraction at interface. Many materials have a well-characterized refractive index, but these indices often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength (λ) of 589 nanometers .
2.6 × 10 11 Qs (8.2 × 10 33 years): The smallest possible value for proton half-life consistent with experiment [19] 10 23 Qs ( 3.2 × 10 45 years ): The largest possible value for the proton half-life , assuming that the Big Bang was inflationary and that the same process that made baryons predominate over antibaryons in the early Universe ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
The values for a/b·2π can be found by applying de Moivre's identity for n = a to a b th root of unity, which is also a root of the polynomial x b - 1 in the complex plane. For example, the cosine and sine of 2π ⋅ 5/37 are the real and imaginary parts , respectively, of the 5th power of the 37th root of unity cos(2π/37) + sin(2π/37)i ...