trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles...

spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous...

the cosine of the angle θ between the observer's line of sight and the surface normal; I = I0 cos θ. The law is also known as the cosine emission law or...

and angles in scalene triangles, with the other being the law of cosines. The law of sines can be generalized to higher dimensions on surfaces with constant...

the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from...

written using cosines (sometimes called the spherical law of cosines, not to be confused with the law of cosines for plane geometry) instead of haversines...

+\beta )}}.} 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...

circumradius. The law of cosines is useful for computing the length of an unknown side if two other sides and an angle are known. The law states, a 2 + b...

accessible enclosed distance. The law of cosines (also known as the cosine formula or cosine rule) is an extension of the Pythagorean theorem: c 2 = a...

\\\end{aligned}}} which is the law of cosines. There are two ternary operations involving dot product and cross product. The scalar triple product of three vectors is...

equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the cosine value unambiguously determines its...

law. In the parallelogram on the right, let AD = BC = a, AB = DC = b, ∠ B A D = α . {\displaystyle \angle BAD=\alpha .} By using the law of cosines in...

{b}{R}}} where cosh is the hyperbolic cosine. This formula is a special form of the hyperbolic law of cosines that applies to all hyperbolic triangles:...

{(a+b+c)(a-b+c)(a+b-c)(b+c-a)}}}.} The law of cosines (known as the cosine formula, or the "cos rule") is an extension of the Pythagorean theorem to arbitrary...

)\sin(\angle \mathrm {BPC} )}}} This can be deduced from the spherical law of cosines. Atropisomer "Angle Between Two Planes". TutorVista.com. Archived from...

faces of the tetrahedron adjacent to the edge P i P j {\displaystyle P_{i}P_{j}} . The law of cosines for a tetrahedron, which relates the areas of the...

law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in...

{\displaystyle \gamma } ⁠ the angles opposite those sides. Applying the law of cosines we get cos ⁡ γ = a 2 + b 2 − c 2 2 a b {\displaystyle \cos \gamma ={\frac...

the Earth, the cosine of the central angle is near 0.99999999). For modern 64-bit floating-point numbers, the spherical law of cosines formula, given...

two proofs of the cosine rule (Articles 37 and 60) and two proofs of the sine rule (Articles 40 and 42). The page on Spherical law of cosines gives four...

polarization of an algebraic form. Inner product space – Generalization of the dot product; used to define Hilbert spaces Law of cosines – Property of all triangles...

be derived from the law of cosines in trigonometry. In a right triangle, the cosine of an angle is the ratio of the leg adjacent of the angle and the hypotenuse...

consequence of – another existing theorem. The 'Porism' can be viewed on pages 36 and 37 of DROC (Harvard electronic copy) "Sine, Cosine, and Ptolemy's...

two segments of equal length), the result is known as Apollonius' theorem. The theorem can be proved as an application of the law of cosines. Let θ be the...

+\cot \beta ={\frac {c}{h_{c}}}.} The law of cosines can be expressed in terms of the cotangent instead of the cosine, which brings the triangle's area S...

tetrahedra is 5-dimensional. See: Law of sines The law of cosines for the tetrahedron relates the areas of each face of the tetrahedron and the dihedral...

specific trigonometric laws or formulas. For instance, propositions twelve and thirteen of book two of the Elements are the laws of cosines for obtuse and acute...

the trigonometric identity). Solving for common side DB, in △ADB and △BDC, the law of cosines gives p 2 + q 2 − 2 p q cos ⁡ A = r 2 + s 2 − 2 r s cos ⁡ C . {\displaystyle...

proved using vectors (see parallelogram law). The following is an independent proof using the law of cosines. Let the triangle have sides a , b , c {\displaystyle...

to the relation of Pythagorean triples to the Gaussian integers. Triangles with an angle of 60° are a special case of the Law of Cosines: c 2 = a 2 − a...