import numpy as np

def dcum(a, b, t):
    """
    计算 PROSAIL 中使用的累积分布函数 dcum
    
    Parameters:
    - a: float
    - b: float
    - t: float, in degrees

    Returns:
    - f: float
    """
    rd = np.pi / 180  # degree to radian
    if a >= 1:
        f = 1 - np.cos(rd * t)
    else:
        eps = 1e-8
        x = 2 * rd * t
        p = x
        delx = 1.0
        while delx >= eps:
            y = a * np.sin(x) + 0.5 * b * np.sin(2 * x)
            dx = 0.5 * (y - x + p)
            x += dx
            delx = abs(dx)
        f = (2 * y + p) / np.pi
    return f