# Complex Computations, Trigonometric Functions

Sine: Sin(x) = {Sin(x.r) * Cosh(x.i), Cos(x.r) * Sinh(x.i)}
See: Sine -- From MathWorld
and Wolfram Function Evaluation

Cosine: Cos(x) = {Cos(x.r) * Cosh(x.i), −Sin(x.r) * Sinh(x.i)}
See: Cosine -- From MathWorld
and Wolfram Function Evaluation

Tangent: Tan(x) = {Sin(2*x.r)/d, Sinh(2*x.i)/d}
where d = Cos(2*x.r) + Cosh(2*x.i)
and x is not equivalent to plus or minus 90 degrees.
See: Tangent -- From MathWorld
and Wolfram Function Evaluation

Cotangent: Cot(x) = {Sin(2*x.r)/d, −Sinh(2*x.i)/d}
where d = −Cos(2*x.r) + Cosh(2*x.i)
and x is not equivalent to zero or 180 degrees.
See: Cotangent -- From MathWorld
and Wolfram Function Evaluation

Secant: Sec(x) = {Coth(x.i)/d, Tan(x.r)/d}
where d = Sec(x.r)*Sinh(x.i) + Cos(x.r)*Csch(x.i)
and x is not equivalent to plus or minus 90 degrees.
See: Secant -- From MathWorld
and Wolfram Function Evaluation

Cosecant: Csc(x) = {Coth(x.i)/d, −Cot(x.r)/d}
where d = Sin(x.r)*Csch(x.i) + Csc(x.r)*Sinh(x.i)
and x is not equivalent to zero or 180 degrees.
See: Cosecant -- From MathWorld
and Wolfram Function Evaluation