ComplexTrigonometricX<T extends Complex> extension
A collection for trigonometric for Complex
Sine
Compute the sine of this complex number.
Implements the formula:
sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.
Returns nan if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
sin(1 ± INFINITY i) = 1 ± INFINITY i
sin(±INFINITY + i) = NaN + NaN i
sin(±INFINITY ± INFINITY i) = NaN + NaN i
Cosine
Compute the cosine of this complex number.
Implements the formula:
cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i
where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.
Returns nan if either real or imaginary part of the
input argument is NaN.
Infinite values in real or imaginary parts of the input may result in
infinite or NaN values returned in parts of the result.
Examples:
cos(1 ± INFINITY i) = 1 ∓ INFINITY i
cos(±INFINITY + i) = NaN + NaN i
cos(±INFINITY ± INFINITY i) = NaN + NaN i
Tangent
Compute the tangent of this complex number.
Implements the formula:
tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.
Returns nan if either real or imaginary part of the
input argument is NaN.
Infinite (or critical) values in real or imaginary parts of the input may
result in infinite or NaN values returned in parts of the result.
Examples:
tan(a ± INFINITY i) = 0 ± i
tan(±INFINITY + bi) = NaN + NaN i
tan(±INFINITY ± INFINITY i) = NaN + NaN i
tan(±π/2 + 0 i) = ±INFINITY + NaN i
Arcsine
Compute the inverse sine of this complex number.
Implements the formula:
asin(z) = -i (log(sqrt(1 - z^2) + iz))
Returns nan if either real or imaginary part of the
input argument is NaN or infinite.
Arccosine
Compute the inverse cosine of this complex number.
Implements the formula:
acos(z) = -i (log(z + i (sqrt(1 - z^2))))
Returns nan if either real or imaginary part of the
input argument is NaN or infinite.
Arctangent
Compute the inverse tangent of this complex number.
Implements the formula:
atan(z) = (i/2) log((i + z)/(i - z))
Returns nan if either real or imaginary part of the
input argument is NaN or infinite.
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