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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 ...
In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
The new formula is more concentrated and distributed in smaller containers, with a 12.3 US fl oz (360 ml) (348 g (12.3 oz)) making 8 US quarts (7,600 ml). According to the preparation instructions on the 20 fl oz (590 ml) Tang orange drink mix, 2 level tablespoons of Tang can be combined with 1 cup or 8 fl oz (240 ml) of cold water for 1 serving.
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 ...
The kayser (K) is a unit of wavenumber equal to 1 cm −1 (100 m −1). The gal (Gal) is a unit of acceleration equal to 1 cm/s 2. [3] The dyne (dyn) is a unit of force equal to 1 g⋅cm⋅s −2 (10 μN). [3] The barye (Ba) is a unit of pressure equal to 1 dyn⋅cm −2 (100 mPa). The erg (erg) is a unit of energy equal to 1 dyn⋅cm (100 nJ). [3]
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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.