Ncert Exercises & Solutions

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

Hint: Apply the principle of dimension homogeneity.

Since f( $θ$ ) is a sum of different powers of $θ$ and it is a dimensionless quantity.

By the principle of dimension homogeneity, as RHS is dimensionless, hence LHS should also be dimensionless.

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