What is the period of $f (t) = cos (\frac{8 t}{3})$ $f(t)=cos ( ( 8 t ) / 3 )$ ?

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Answer 1 · 2018-08-05T11:15:19

$Period = \frac{3}{4} π$ $color(blue)("Period " = 3/4 pi$

Standard form of cosine function is $f (x) = A cos (B x - C) + D$ $f(x) = A cos(Bx - C) + D$

$Given : f (t) = cos (\frac{8}{3} t)$ $"Given : " f(t) = cos (8/3 t)$

$A = 1, B = \frac{8}{3}, C = D = 0$ $A = 1, B = 8/3, C = D = 0$

$A m p l i t u d e = | A | = 1$ $Amplitude = |A| = 1$

$Period = \frac{2 π}{| B |} = \frac{2 π}{∣ ∣ \frac{8}{3} ∣ ∣} = \frac{3}{4} π$ $"Period " = (2pi) / |B| = (2pi) / |8/3| = 3/4 pi$

$Phase Shift = \frac{- C}{B} = 0$ $"Phase Shift " = (-C) / B = 0$

$Vertical Shift = D = 0$ $"Vertical Shift " = D = 0$

graph{cos (8/3 x) [-10, 10, -5, 5]}

What is the period of f(t)=cos(8t3)f(t)=cos ( ( 8 t ) / 3 ) ?