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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _time_variable_part(epoch, ref_epoch, trnd, periodic):
 """ Return sum of the time-variable part of the coefficients The formula is: G(t) = G(t0) + trnd*(t-t0) + asin1*sin(2pi/p1 * (t-t0)) + acos1*cos(2pi/p1 * (t-t0)) + asin2*sin(2pi/p2 * (t-t0)) + acos2*cos(2pi/p2 * (t-t0)) This function computes all terms after G(t0). """

    delta_t = epoch - ref_epoch
    trend = trnd * delta_t
    periodic_sum = _np.zeros_like(trnd)
    for period in periodic:
        for trifunc in periodic[period]:
            coeffs = periodic[period][trifunc]
            if trifunc == 'acos':
                periodic_sum += coeffs * _np.cos(2 * _np.pi / period * delta_t)
            elif trifunc == 'asin':
                periodic_sum += coeffs * _np.sin(2 * _np.pi / period * delta_t)
    return trend + periodic_sum