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All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.
Ratio. In mathematics, a ratio (/ ˈreɪʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and ...
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant).
v. t. e. Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.
The circle intersects the real axis at 2 (= 1/(1-1/2) when ω 0 t = 0) and at 2/3 (= 1/(1-(-1/2)) when ω 0 t = π). The common ratio can also be a complex number given by | |, where | | is the magnitude of the number as a vector in the complex plane, is the angle or argument of that vector, is Euler's number, and =. In this case, the expanded ...
The water–cement ratio (w/c ratio, or water-to-cement ratio, sometimes also called the Water-Cement Factor, f) is the ratio of the mass of water (w) to the mass of cement (c) used in a concrete mix: The typical values of this ratio f = w⁄c are generally comprised in the interval 0.40 and 0.60. The water-cement ratio of the fresh concrete ...
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The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in ...