The hyperbolic sine and the hyperbolic cosine are entire functions. This relation between sine and cosine is sometimes called the fundamental Pythagorean trigonometric identity. Arctangent interpolation is used to generate rectangular pulses from the sine/cosine signal periods. The cosine and the secant are even functions; the other trigonometric functions are odd functions. The most widely used trigonometric functions are the sine, the cosine, and the tangent. By convention, in-phase modulates cosine and quadrature modulates sine. This complex exponential function is sometimes denoted ("cosine plus i sine"). In complex analysis, the hyperbolic functions arise as the imaginary parts of sine and cosine. The modulation is accomplished by varying the sine and cosine inputs at a precise time. Mathematically, the catenary curve is the graph of the hyperbolic cosine function. TUs use integer basis functions based on the discrete cosine transform (DCT). Two vectors' bits match with probability proportional to the cosine of the angle between them. He also gives a derivation using simple coordinate geometry and the planar cosine rule (Art.60). The canonical correlations formula 98 is equal to the cosine of principal angles. A soft cosine or ("soft" similarity) between two vectors considers similarities between pairs of features.