What is the tangent formula?

The formula for the tangent of an angle, x, is tan(x) = opposite / adjacent, where opposite and adjacent refer to the sides of a right angle triangle containing the angle x. Another formula for the tangent of an angle is tan(x) = sin(x) / cos(x).

The tangent of x can also be written in terms of exponential functions, as tan(x) = i(e^(-ix) - e^(ix))/(e^(-ix) + e^(ix)), where e is the fundamental constant approximately equal to 2.72. The function tan(x) is periodic with a period of pi, which means that the formula tan(x + pi) = tan(x) is always true.