Question
A function $\text{f}(\theta)$ is defined as:
$\text{f}(\theta)=1-\theta+\frac{\theta^2}{2!}-\frac{\theta^3}{3!}+\frac{\theta^4}{4!}$
Why is it necessary for q to be a dimensionless quantity?✓
Answer
$\theta$ is represented by angle which is equal to $\frac{\text{arc}}{\text{radius}}$ so angle $\theta$ is dimensionless physical quantity.
First term is 1 which is dimensionless, next term contain only powers of $\theta$, as $\theta$ is dimensionless so their powers will also be dimensionless. Hence, each term in R.H.S. expression are dimensionless so left hand side $\text{f}(\theta)$ must be dimensionless.
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