$A$ function $f(\theta)$ is defined as $f(\theta) = 1 - \theta + \frac{\theta^2}{2!} - \frac{\theta^3}{3!} + \frac{\theta^4}{4!} - \dots$. Why is it necessary for $f(\theta)$ to be a dimensionless quantity?

(N/A) The given function $f(\theta)$ is a power series expansion of the exponential function $e^{-\theta}$.
In any physical equation,terms added or subtracted must have the same dimensions.
Since the first term is a dimensionless constant $(1)$,all subsequent terms $(\theta, \frac{\theta^2}{2!}, \dots)$ must also be dimensionless.
Furthermore,the principle of homogeneity of dimensions states that the arguments of transcendental functions (like exponential,trigonometric,or logarithmic functions) must be dimensionless.
Therefore,for the expression to be physically meaningful,$f(\theta)$ must be a dimensionless quantity.