Sinusoidal Equation

sinusoidal_equation(first_constant, second_constant, third_constant, fourth_constant, precision=4)

Generates a sinusoidal function to provide evaluations at variable inputs

Parameters

  • first_constant (int or float) – Vertical stretch factor of the resultant sine function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • second_constant (int or float) – Horizontal stretch factor of the resultant sine function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • third_constant (int or float) – Horizontal shift of the resultant sine function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • fourth_constant (int or float) – Vertical shift of the resultant sine function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

  • TypeError – First four arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

evaluation – Function for evaluating a sinusoidal equation when passed any integer or float argument

Return type

func

See also

sinusoidal_derivatives(), sinusoidal_integral(), sinusoidal_roots(), sinusoidal_model()

Notes

  • Standard form of a sinusoidal function: \(f(x) = a\cdot{\sin(b\cdot(x - c))} + d\)

    • Period of function: \(\frac{2\pi}{|b|}\)

    • Amplitude of function: \(|a|\)

  • Sine Functions

Examples

Import sinusoidal_equation function from regressions library
>>> from regressions.analyses.equations.sinusoidal import sinusoidal_equation
Create a sinusoidal function with coefficients 2, 3, 5, and 7, then evaluate it at 10
>>> evaluation_first = sinusoidal_equation(2, 3, 5, 7)
>>> print(evaluation_first(10))
8.3006
Create a sinusoidal function with coefficients 7, -5, -3, and 2, then evaluate it at 10
>>> evaluation_second = sinusoidal_equation(7, -5, -3, 2)
>>> print(evaluation_second(10))
-3.7878
Create a sinusoidal function with all inputs set to 0, then evaluate it at 10
>>> evaluation_zero = sinusoidal_equation(0, 0, 0, 0)
>>> print(evaluation_zero(10))
0.0001