Periodic function...??!!

Algebra Level 3

If f(x) = s i n 2 x + c o s 2 x − 2 sin^2x + cos^2x-2 . What you say about its periodicity ?

Note : here i mean to say "period" is to "fundamental period".

Wanna try more problems on functions ?
periodic with period pie periodic with period 2 pie periodic but period not defined not periodic

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Sandeep Bhardwaj
Sep 27, 2014

Given

f ( x ) = ( s i n x ) 2 + ( c o s x ) 2 − 2 f(x)=(sinx)^{2}+(cosx)^{2}-2

==> f ( x ) = 1 − 2 f(x)=1-2

Because ( s i n x ) 2 + ( c o s x ) 2 = 1 (sinx)^{2}+(cosx)^{2}=1 ; whatever be the value of x x

so f ( x ) = − 1 f(x)=-1 i.e. a constant function

A constant function is periodic but its fundamental period is not defined

9 Helpful 0 Interesting 0 Brilliant 0 Confused
Joel Tan
Sep 25, 2014

It is equal to 0 by laws of trigonometry regardless of x.

Another method is elimination: there's no pie in trigonometry so we are left with 2 options. It would definitely be periodic since sin and cos are periodic, hence we get the answer (ii)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It is equal to -1. Not zero.

Vedant Ladha - 6 years, 3 months ago

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