Grade 12Trigonometry

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

Avinash k

11 Years agoGrade 12

2 Answers

Sunil Kumar FP

11 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

Approved Tutor Answer11 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|
$\frac{\pi }{2}$