Tangent minus alpha is equal to minus tangent alpha.įormulas for the reduction of the double angle (sine, cosine, tangent and cotangent of the double angle) The cosine of 'minus alpha' will give the same value as the cosine of the alpha angle. The sine of the negative angle is equal to the negative value of the sine of the same positive angle (minus the sine alpha). In order to get rid of the negative value of the degree angle measure in calculating the sine, cosine or tangent, we can use the following trigonometric transformations (identities), based on the principles of parity or odd trigonometric functions.Īs you can see, the cosine and secant is an even function, the sine, tangent and cotangent are odd functions. Transformation of the negative angles of trigonometric functions (parity and oddness) The product of the tangent per cotangent of the same angle is one (Formula 7). The unit plus the cotangent of the angle is equal to the quotient of the unit divided by the sine square of this angle (Formula 6) The sum of the unit and the tangent of the angle is equal to the ratio of one to the square of the cosine of this angle (Formula 5) see also the proof of the sum of the squares of the cosine and the sine. The sum of the squares of the sine and cosine of the same angle is one (Formula 4). The angle of the angle is equal to one divided by the cosine of the same angle (Formula 3) The quotient of the cosine of the angle α to the sine of the same angle is equal to the cotangent of the same angle (Formula 2) See also the proof of the correctness of the transformation of the simplest trigonometric identities. The quotient of the sine of the alpha angle by the cosine of the same angle is equal to the tangent of this angle (Formula 1). To solve some problems, the table of trigonometric identities will be useful, which will make it much easier to perform the transformation of functions:

Sin cos and tan formula