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Question
A function f(θ) is defined as: `f(θ) = 1 - θ + θ^2/(2!) - θ^3/(3!) + θ^4/(4!)` Why is it necessary for q to be a dimensionless quantity?
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Solution
Here the angle which is represented by θ is equal to `(arc)/(radius)`
`θ = L/L` = no unit
Thus, it is a dimensionless physical quantity. In this expression, the first term is a constant i.e., a numerical value which is dimensionless. The next term is θ that is dimensionless. Similarly, each term in the R.H.S. expression is dimensionless which makes f(θ) of L.H.S. dimensionless.
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