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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 ...
The tonne (/ t ʌ n / ⓘ or / t ɒ n /; symbol: t) is a unit of mass equal to 1,000 kilograms.It is a non-SI unit accepted for use with SI.It is also referred to as a metric ton in the United States to distinguish it from the non-metric units of the short ton (United States customary units) and the long ton (British imperial units).
The tonne (t) is an SI-compatible unit of mass equal to a megagram (Mg), or 10 3 kg. The unit is in common use for masses above about 10 3 kg and is often used with SI prefixes. For example, a gigagram ( Gg ) or 10 9 g is 10 3 tonnes, commonly called a kilotonne .
Harbour ton, used in South Africa in the 20th century, was equivalent to (2,000 pounds (907 kg)) or 1 short ton. Assay ton (abbreviation 'AT') is not a unit of measurement but a standard quantity used in assaying ores of precious metals. A short assay ton is approximately 29.17 g (1.029 oz) and a long assay ton is approximately 32.67 g (1.152 oz).
It was originally defined as the rate of heat transfer that results in the freezing or melting of 1 short ton (2,000 lb; 907 kg) of pure ice at 0 °C (32 °F) in 24 hours. [1] [2] The modern definition is exactly 12,000 Btu IT /h (3.516853 kW). Air-conditioning and refrigeration equipment capacity in the U.S. is often specified in "tons" (of ...
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10 −34 when expressed in the unit J⋅s, which is equal to kg⋅m 2 ⋅s −1, where the metre and the second are defined in terms of c and Δν Cs. —
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In this right triangle, denoting the measure of angle BAC as A: sin A = a / c ; cos A = b / c ; tan A = a / b . Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labeled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point.