Question

$\frac{f}{ \alpha } = (sin \: \beta \: t)$
Find value of α&β​

Answer 1

Answer :-

✨Given that :-

$\dfrac{f}{\alpha} = sin\beta \: t$

◾As we know that :-

$f = \dfrac{1}{t}$

or

$frequency = \dfrac{1}{time\: period}$

◾Now we will substitute $f = \dfrac{1}{t}$.

$\dfrac{f}{\alpha} = sin\beta \: t$

$\implies \dfrac{\dfrac{1}{t}}{\alpha} = sin\beta \: t$

$\implies \dfrac{1}{\alpha\times t} = sin\beta \: t$

$\implies \dfrac{1}{\alpha\times t^2} = sin\beta$

$\implies \dfrac{1}{t^2} = \alpha \times sin\beta$

$\implies \dfrac{1}{t} \times \dfrac{1}{t} = \alpha \times sin\beta$

◾By using hit and trial we conclude

$\longrightarrow sin\beta = \alpha$

▪️Then

$\alpha = \dfrac{1}{t} = sin\beta$

Or

$\alpha = f = sin\beta$

⏩Verification :-

$\dfrac{f}{\alpha} = sin\beta \: t$

$\implies \dfrac{f}{f} = f \times t$

$\implies 1 = f \times \dfrac{1}{f}$

$\implies 1 = 1$

✨Hence ,RHS = LHS