Question

$\bf \: If \: f(t) = 50 sin ( 100 π + 0.4 ) Then \: \: ST \: \: f( \frac{1}{50} + 1) = f(t)$

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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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Answer 2

Based on the proof, the function $f(\frac{1}{50} +t)$ is equal to f(t).

What is a function?

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable.

Given the following function:

• $f(t)=50sin(100 \pi t+0.4)$

In this exercise, you are required to show that the given function is equal to $f(\frac{1}{50} +t)$.

Substituting for t, we have:

$f(\frac{1}{50} +t)=50sin(100 \pi (\frac{1}{50} +t)+0.4)\\\\f(\frac{1}{50} +t)=50sin( \frac{100 \pi}{50} +100 \pi t+0.4)\\\\f(\frac{1}{50} +t)=50sin(100 \pi t+0.4)\\\\f(\frac{1}{50} +t)=f(t)$

Read more on function here: https://brainly.com/question/4246058