Question

If
f (t) = 50 sin (100π+ 0.4), prove that
f(1/50+ t) = f(t).​

Answer 1

Answer:

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Answer 2

SOLUTION

GIVEN

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

TO PROVE

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

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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