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  • The period of sin pi[x]/12+cos pi[x]/4+tan pi[x]/3 where [x] repersents the greatest integer less than or equal to x is .

The period of sin pi[x]/12+cos pi[x]/4+tan pi[x]/3 where [x] repersents the greatest integer less than or equal to x is .

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Solution: Since,

\ Rightarrow hspace1cmsinpi [x+24]/12=sinpi /12(24+[x])\ \Rightarrow hspace1cmsin(2pi +pi [x]/2)=sinpi [x]/12

The period of sinpi [x]/12 is 24.

Similarly , period of cospi [x]/4 is 8 and period of tanpi [x]/3 =3

Hence , the period of the given function =LCM of 24,8,3=24

Posted by

Deependra Verma

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