A DERIVATION METHOD FOR THE EXACT VALUES OF SINE AND COSINE OF 1° AND ANY INTEGER DEGREE

A set of meticulously designed procedures and ingenious methods for calculating the exact values of sine/cosine for 1° and any integer degree has been discovered and constructed. By calculating the sine/cosine values for 3°, and then using the expansion formulas for sine/cosine of triple angles, a univariate cubic equation satisfied by the sine/cosine values of 1° is derived. Subsequently, the exact expressions for sin/cos 1° are determined using Cardano's formula and its discriminant rules. After calculating the exact values of sine/cosine for all integer degrees up to 45° in the form of 3k°, the exact expressions for sine/cosine of all angles in the form of 3k±1° are calculated, and a table of exact sine/cosine values for any integer degree is compiled.