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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 quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
The standard unit is the meter cubed per kilogram (m 3 /kg or m 3 ·kg −1). Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the unit is the centimeter cubed per gram (cm 3 /g or cm 3 ·g −1). To convert m 3 /kg to cm 3 /g, multiply by 1000; conversely ...
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
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The angle between the horizontal line and the shown diagonal is 1 / 2 (a + b). This is a geometric way to prove the particular tangent half-angle formula that says tan 1 / 2 (a + b) = (sin a + sin b) / (cos a + cos b). The formulae sin 1 / 2 (a + b) and cos 1 / 2 (a + b) are the ratios of the actual distances to ...
The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380 649 × 10 −23 J⋅K −1, (J = kg⋅m 2 ⋅s −2), given the definition of the kilogram, the metre, and the second.
The centimetre (SI symbol: cm) is a unit of length in the metric system equal to 10 −2 metres ( 1 / 100 m = 0.01 m). To help compare different orders of magnitude, this section lists lengths between 10 −2 m and 10 −1 m (1 cm and 1 dm). 1 cm – 10 millimeters; 1 cm – 0.39 inches; 1 cm – edge of a square of area 1 cm 2