Sums of sines and cosines arise in Fourier series. The sines and cosines in the Fourier series are an example of an orthonormal basis. 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. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines. The value involving hyperbolic sines is similarly denoted , when . Theorems on the lengths of chords are applications of the law of sines. A direct application of the law of sines to Figure 3 produces Equation . See curved variations of the Law of Sines to see details of this derivation. This formula uses the law of sines. The angle of this change can be determined using the law of sines. The following are examples of how to solve a problem using the law of sines. SVA elements are present at lower levels than SINES and LINEs in humans. Madhava composed an accurate table of sines.