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Grade 12Trigonometry

Period of f(x)= [sin3x]+|cos 6x|
Please explain particularly about sin 3x period

Profile image of Priya
8 Years agoGrade 12
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1 Answer

Profile image of Arun
8 Years ago
Dear Priya
f(x) = [sin(3x)] + |cos(6x)|
f(x) = f_{1}(x) + f_{2}(x)
f_{1}(x) = [sin(3x)]
= 0, 0\leq x\leq \frac{\pi }{3}
= -1, \frac{\pi }{3}\leq x\leq \frac{2\pi }{3}
Time period of f1(x):
\frac{2\pi }{3} = \frac{4\pi }{6}
f_{2}(x) = |cos(6x)|
Time period of f2(x):
\frac{\pi }{6}
Time period of f(x):
(LCM of time period of f1(x) & f2(x))/(HCFof time period of f1(x) & f2(x))
\frac{4\pi }{6} = \frac{2\pi }{3}
 
 
In case of any difficulty, plese feel free to ask.
 
Regards
Arun

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