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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 β.
which by the Pythagorean theorem is equal to 1. This definition is valid for all angles, due to the definition of defining x = cos θ and y sin θ for the unit circle and thus x = c cos θ and y = c sin θ for a circle of radius c and reflecting our triangle in the y-axis and setting a = x and b = y.
Zinc borate refers to a family of inorganic compounds consisting of borate of zinc.They are white solids with the formulas 4ZnO·B 2 O 3 ·H 2 O, ZnO·B 2 O 3 ·1.12H 2 O, ZnO·B 2 O 3 ·∼2H 2 O, 6ZnO·5B 2 O 3 ·3H 2 O, 2ZnO·3B 2 O 3 ·7H 2 O, 2ZnO·3B 2 O 3 ·3H 2 O, 3ZnO·5B 2 O 3 ·14H 2 O, and ZnO·5B 2 O 3 ·4.5H 2 O.
In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...
For gases, departure from 3 R per mole of atoms is generally due to two factors: (1) failure of the higher quantum-energy-spaced vibration modes in gas molecules to be excited at room temperature, and (2) loss of potential energy degree of freedom for small gas molecules, simply because most of their atoms are not bonded maximally in space to ...
A polar covalent bond exists between carbon and zinc, being polarized toward carbon due to the differences in electronegativity values (carbon: 2.5 & zinc: 1.65). The dipole moment of symmetric diorganozinc reagents can be seen as zero in these linear complexes, which explains their solubility in nonpolar solvents like cyclohexane .
For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be called a "2 normal" solution.
Just as for the trigonometric functions, values of the lemniscate functions can be computed for divisions of the lemniscate into n parts of equal length, using only basic arithmetic and square roots, if and only if n is of the form = where k is a non-negative integer and each p i (if any) is a distinct Fermat prime.
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