What is the period of $f (t) = cos (\frac{7 t}{2})$ $f(t)=cos ( ( 7 t ) / 2 )$ ?

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Answer 1 · 2016-05-16T06:52:51

$\frac{4 π}{7}$ $(4pi)/7$ .

The period for both sin kt and cos kt is (2pi)/k.

Here, k = = $\frac{7}{2}$ $7/2$ . So, the period is $4 π \frac{)}{7} .$ $4pi)/7.$ .

See below how it works

$cos ((\frac{7}{2}) (t + \frac{4 π}{7})) = cos (\frac{7 t}{2} + 2 π) = cos (\frac{7 t}{2})$ $cos ((7/2)(t+(4pi)/7))=cos((7t)/2+2pi)=cos((7t)/2)$

Answer 2 · 2016-05-16T07:53:52

$T = \frac{4 π}{7}$ $T=(4pi)/7$

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$y = A \cdot cos (ω \cdot t + ϕ) general equation$ $y=A*cos(omega*t+phi)" general equation"$

$A:Amplitude$ $"A:Amplitude"$

$ω : Angular velocity$ $omega:"Angular velocity"$

$ϕ = phase angle$ $phi="phase angle"$

$your equation: f (t) = cos (\frac{7 t}{2})$ $"your equation:" f(t)=cos((7t)/2)$

$A = 1$ $A=1$

$ω = \frac{7}{2}$ $omega=7/2$

$ϕ = 0$ $phi=0$

$ω = \frac{2 π}{T} T:Period$ $omega=(2pi)/T" T:Period"$

$\frac{7}{2} = \frac{2 π}{T}$ $7/2=(2pi)/T$

$T = \frac{4 π}{7}$ $T=(4pi)/7$

What is the period of f(t)=cos(7t2)f(t)=cos ( ( 7 t ) / 2 ) ?