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Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of sines states that a/(sinA)=b/(sinB)=c/(sinC)=2R, (1) where R is the ...

Let a triangle have sides of length a, b, and c and let the angles opposite these sides be denoted A, B, and C. The law of tangents states ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

A spherical harmonic of the form sin(mphi)P_m^m(costheta) or cos(mphi)P_m^m(costheta).

Let a spherical triangle have sides of length a, b, and c, and semiperimeter s. Then the spherical excess E is given by

Trigonometry