A function f(θ) is defined as: f(θ) = 1 – θ +\(\frac{\theta^2}{2!

1.	A function f(θ) is defined as: f(θ) = 1 – θ +\(\frac{\theta^2}{2!}\)- \(\frac{\theta^3}{3!}\) +\(\frac{\theta^4}{4!}\)... Why is it necessary for f(θ) to be a dimensionless quantity?
Answer» Since f(θ) is a sum of different powers of θ, it has to be dimensionless, then LHS should also be dimensionless. According to homogeneity principle, if RHS is dimensionless, then LHS should also be dimensionless.

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

Answer»

Since f(θ) is a sum of different powers of θ, it has to be dimensionless, then LHS should also be dimensionless.

According to homogeneity principle, if RHS is dimensionless, then LHS should also be dimensionless.