Trigonometric numbers are irrational cosines or sines of angles that are rational multiples of . Sums of sines and cosines arise in Fourier series. Each of these 3 differential equations has the same solution&colon; sines, cosines or complex exponentials. The version with sines and cosines is also justified with the Hilbert space interpretation. Regiomontanus's table of sines and cosines was published in 1533. In 1533, Regiomontanus's table of sines and cosines were published. The page on Spherical law of cosines gives four different proofs of the cosine rule. This formula is the law of cosines, sometimes called the generalized Pythagorean theorem. A purely algebraic proof can be constructed from the spherical law of cosines.. Three of these numbers are the direction cosines that orient the eigenvector. The theorem can be proved as an application of the law of cosines. These formulas are a direct consequence of the law of cosines. Because of time reversal symmetry, only even powers of the cosines are allowed. The direction cosines of the position vector provide a quantitative measure of direction. One can also prove the law of cosines by calculating areas.