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

A function f(\theta ) is defined as

f(\theta )= 1-\theta +\frac{\theta ^{2}}{2!}-\frac{\theta ^{3}}{3!}+\frac{\theta ^{4}}{4!}+.........

Why is it necessary for \theta to be a dimensionless quantity ?

Answers (1)

(i) \theta is a dimensionless physical quantity since it is represented by an angle viz. equal to arc/radius.

(ii) As \theta is dimensionless, all its powers will also be dimensionless. Here the first term is 1 viz. also dimensionless.

Hence, the L.H.S. f(\theta) must be dimensionless so that all the terms in R.H.S. are also dimensionless.

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