I’m not sure it will work everywhere, but for sin(x), one can write sin(x) = x/(1 radian)! - x³/(3 radians)! + … = x/(1 radian) - x³/(1 radian × 2 radian

I’m not sure it will work everywhere, but for sin(x), one can write sin(x) = x/(1 radian)! - x³/(3 radians)! + … = x/(1 radian) - x³/(1 radian × 2 radians × 3 radians) + … That makes the ‘radians’ units cancel out.