Question

0%29%20Then%20%5C%3A%20%5C%3A%20ST%20%5C%3A%20%5C%3A%20f%28%20%5Cfrac%7B1%7D%7B50%7D%20%2B%201%29%20%3D%20f%28t%29%20" id="TexFormula1" title=" \bf \: If \: f(t) = 50 sin ( 100 π + 0.4 ) Then \: \: ST \: \: f( \frac{1}{50} + 1) = f(t) " alt=" \bf \: If \: f(t) = 50 sin ( 100 π + 0.4 ) Then \: \: ST \: \: f( \frac{1}{50} + 1) = f(t) " align="absmiddle" class="latex-formula">
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Thank You! :)

Answer 1

PROOF

Here it is given that

$\displaystyle \sf{f(t) = 50 \: \sin(100\pi t+ 0.4)}$

Now

$\displaystyle \sf{f \bigg( \frac{1}{50} + t \bigg) }$

$\displaystyle \sf{ = 50 \: \sin \Bigg[100\pi \bigg( \frac{1}{50} + t \bigg)+ 0.4 \Bigg] }$

$\displaystyle \sf{ = 50 \: \sin \Bigg[ \bigg(100\pi \times \frac{1}{50} + 100\pi t \bigg)+ 0.4 \Bigg] }$

$\displaystyle \sf{ = 50 \: \sin \Bigg[ \bigg(2\pi + 100\pi t \bigg)+ 0.4 \Bigg] } \\ \\ \displaystyle \sf{ = 50 \: \sin ( 100\pi t + 0.4 ) }$

$\sf{ = f(t)}$

Hence proved

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