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A function f(theta) is defined as : f(th...

A function `f(theta)` is defined as : `f(theta) = 1 - theta+(theta^2)/(2!) - (theta^3)/(3!) +(theta^4)/(4!)….` why is it necessary for `theta` to be a dimensionless quantity ?

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`Here, f(theta) = 1 +(theta^2)/(2!) - (theta^3)/(3!)+ (theta^4)/(4!) - …… .`
As `f(theta)` is sum of different powers of `theta,` therefore `theta` must be dimensionless. This is because quantities having different dimensions cannot be added.
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Knowledge Check

  • If: f(theta)=log((1+theta)/(1-theta)), then: f((2theta)/(1+theta^2))=

    A
    `[f(theta)\]^2`
    B
    `[f(theta)]^3`
    C
    `2.f(theta)`
    D
    `3.f(theta)`

  • If f(theta)=sin theta(sin theta+sin 3 theta ) , then f (theta)

    A
    `ge0` only when `theta ge0`
    B
    `le 0` for all real `theta`
    C
    `ge 0` for all real `theta`
    D
    `le 0` only when `theta le 0`

  • Let f(theta)=sin theta(sin theta +sin 3 theta). " Then " f(theta)

    A
    ` ge 0," only when " theta ge 0`
    B
    `le 0," for all real " theta`
    C
    `ge 0," for all real " theta`
    D
    `le 0," only when " theta le 0`

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