Complex trig functions

Complex valued special functions about a point.

boring_math.special_functions.trigonometry.ctrig0.csin0(z: complex, /, n: int = depth) → complex

Partially factored Taylor expansion of sine about z = 0.

Note

Best if |z| <= 2π and n >= 20.

Parameters:

• z – independent variable

• n – terms in expansion, must have 2 <= n <= 84

Returns:

Taylor series expansion of sine(x) centered at z = 0.

boring_math.special_functions.trigonometry.ctrig0.ccos0(z: complex, /, n: int = depth) → complex

Partially factored Taylor expansion of cosine about z = 0.

Note

Best if |z| <= 2π and n >= 22.

Parameters:

• z – independent variable

• n – terms in expansion, must have 2 <= n <= 84

Returns:

Taylor series expansion of cosine(z) centered at z = 0

boring_math.special_functions.trigonometry.ctrig0.ctan0(z: complex, /, n: int = depth) → complex

Tangent centered about z = 0.

Note

Best if |z| <= π and n >= 20.

Parameters:

• z – Independent variable.

• n – Terms in expansion, must have 2 <= n <= 84.

Returns:

The value csin0(z)/ccos0(z).

Complex valued trig functions.

boring_math.special_functions.trigonometry.ctrig.csin(z: complex, /, n: int = depth) → complex

Complex sine valid for all z∈ℂ.

Parameters:

• z – Independent variable.

• n – Terms in expansion, must have 2 <= n <= 84.

Returns:

Value of sine(z).

boring_math.special_functions.trigonometry.ctrig.ccos(z: complex, /, n: int = depth) → complex

Complex cosine valid for all z∈ℂ.

Parameters:

• z – Independent variable.

• n – Terms in expansion, must have 2 <= n <= 84.

Returns:

Value of cosine(z).

boring_math.special_functions.trigonometry.ctrig.ctan(z: complex, /, n: int = depth) → complex

Complex tangent valid for all z∈ℂ.

Parameters:

• z – Independent variable.

• n – Terms in expansion, must have 2 <= n <= 84.

Returns:

Value of tangent(z) via sine(z)/cosine(z).