Relates tangents of two angles of a triangle and the lengths of the opposing sides
Figure 1 – A triangle. The angles α, β, and γ are respectively opposite the sides a, b, and c.
Trigonometry
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Generalized trigonometry
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Unit circle
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In trigonometry, the law of tangents or tangent rule[1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.
In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective sides. The law of tangents states that
The law of tangents, although not as commonly known as the law of sines or the law of cosines, is equivalent to the law of sines, and can be used in any case where two sides and the included angle, or two angles and a side, are known.
^See Eli Maor, Trigonometric Delights, Princeton University Press, 2002.
the lawoftangents or tangent rule is a statement about the relationship between the tangentsof two angles of a triangle and the lengths of the opposing...
the sine, the cosine, and the tangentof a sum or a difference of two angles in terms of sines and cosines and tangentsof the angles themselves. These...
spherical triangles, discovered the lawoftangents for spherical triangles, and provided proofs for both these laws. Knowledge of trigonometric functions and...
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\,\cot \gamma =1.} Lawof sines Lawof cosines Lawoftangents Mollweide's formula Heron's formula The Universal Encyclopaedia of Mathematics, Pan Reference...
=\arccos \left({\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right)} The lawoftangents, or tangent rule, can be used to find a side or an angle when two sides and...
the lawoftangents for spherical triangles, and provided proofs for both these laws. Nasir al-Din al-Tusi has been described as the creator of trigonometry...
precise terms, using three or more lines of position is still correctly called resection, as angular lawoftangents (cot) calculations are not performed)...
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identities follow by division of the Delambre formulae. (Todhunter, Art.52) Taking quotients of these yields the lawoftangents, first stated by Persian mathematician...
Details of Fresnel's derivation, including the modern forms of the sine law and tangentlaw, were given later, in a memoir read to the French Academy of Sciences...
Law of cosines Lawof cotangents Lawof sines Lawoftangents List of integrals of inverse trigonometric functions List of integrals of trigonometric functions...
theory, the lawof large numbers (LLN) is a mathematical theorem that states that the average of the results obtained from a large number of independent...
Gospel Tangents video interview with Wilde. YouTube. 3 November 2017. Retrieved 16 August 2019. "FLDS-Centennial Park Rivalry". Gospel Tangents video interview...
(extract, published 1823). See especially pp. 773 (sine law), 757 (tangentlaw), 760–61 and 792–6 (angles of total internal reflection for given phase differences)...
Intuitively this is summing up all vector components in line with the tangents to the curve, expressed as their scalar products. For example, given a...
rather than derivatives and tangents (see The Method of Mechanical Theorems). The use of infinitesimals to compute rates of change was developed significantly...
of sine, cosine, tangent, and other trigonometric functions for various angles. These angles are usually arranged across the top row of the table, while...
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