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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.
1. Means "less than or equal to". That is, whatever A and B are, A ≤ B is equivalent to A < B or A = B. 2. Between two groups, may mean that the first one is a subgroup of the second one. ≥ 1. Means "greater than or equal to". That is, whatever A and B are, A ≥ B is equivalent to A > B or A = B. 2.
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 ...
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 ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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 ...
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.
[1] [10] Another precarious convention used by a small number of authors is to use an uppercase first letter, along with a “ −1 ” superscript: Sin −1 (x), Cos −1 (x), Tan −1 (x), etc. [11] Although it is intended to avoid confusion with the reciprocal, which should be represented by sin −1 (x), cos −1 (x), etc., or, better, by ...