What is the period of $f (x) = 0.5 sin (x) cos (x)$ $f(x)=0.5sin(x)cos(x)$ ?

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Answer 1 · 2018-03-08T14:55:19

$P e r i o d = π$ $Period = pi$

$f (x) = y = 0.5 sin x cos x$ $f(x) = y = 0.5 sin x cos x$

$y = (\frac{1}{2}) \frac{2 sin x cos x}{2}$ $y = (1/2) (2sin x cos x) / 2$

$y = (\frac{1}{4}) sin 2 x$ $y = (1/4) sin 2x$

It’s in the form $y = a sin (b x + c) + d$ $y = a sin (bx + c) + d$ where,

$a = \frac{1}{4}, b = 2, c = d = 0$ $a = 1/4, b = 2, c = d = 0$

Amplitude $= a = (\frac{1}{4})$ $= a = (1/4)$

Period $= \frac{2 π}{| b |} = \frac{2 π}{2} = π$ $= (2pi) / |b| = (2pi) / 2 = pi$

graph{0.5 (sin (x) cos (x)) [-10, 10, -5, 5]}

What is the period of f(x)=0.5sin(x)cos(x)f(x)=0.5sin(x)cos(x)f(x)=0.5sin(x)cos(x)?