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what is the periof of modulus of sin(x)cos(x)

what is the periof of modulus of sin(x)cos(x)

Grade:12

2 Answers

Sunil Kumar FP
askIITians Faculty 183 Points
8 years ago
period of sinx and cos x is 2pi
modulus of sinx *cosx
=2*sinxcosx/2
=2*modulus of sin2x
period of sin2x=2pi/2=pi

thus its period is pi
Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

f(x) = |sin(x)cos(x)|
f(x) = |\frac{2}{2}.sin(x)cos(x)|
sin2x = 2sin(x)cos(x)
f(x) = |\frac{sin2x}{2}|
Period of f(x) = sin2x
\frac{2\pi }{2} = \pi
Since we are taking the modulus, then negatib=ve part of the graph will come on +ve side which is similar to the +ve positive side. So period will be reduce by half.
Period of f(x) = |sin2x/2|
\frac{\pi }{2}

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