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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.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
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The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. 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.
SIN-1, Linsidomine (3-morpholinosydnonimine), a drug acting as a vasodilator; sin x−1 = sin(x)−1 = −(1−sin(x)) = −cvs(x) or negative coversine of x, the additive inverse (or negation) of an old trigonometric function; sin −1 y = sin −1 (y), sometimes interpreted as arcsin(y) or arcsine of y, the compositional inverse of the ...
Crossword-like puzzles, for example Double Diamond Puzzles, appeared in the magazine St. Nicholas, published since 1873. [32] Another crossword puzzle appeared on September 14, 1890, in the Italian magazine Il Secolo Illustrato della Domenica. It was designed by Giuseppe Airoldi and titled "Per passare il tempo" ("To pass the time"). Airoldi's ...
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.
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, [1] after the lemniscate curves of a similar shape studied in algebraic geometry, [2] or "lazy eight", in the terminology of livestock branding. [3] This symbol was first used mathematically by John Wallis in the ...