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1. what is period of f(x)=|tanx| + cos 2x ? 2. what is period of function f(x)= log arcsin({x}),here {.} is fractional part function.plzzz do graphically .

1. what is period of f(x)=|tanx| + cos 2x ?


2. what is period of function f(x)= log arcsin({x}),here {.} is fractional part function.plzzz do graphically .

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4 Answers

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Manuj,

 

1. The period of |tanx| = pi.

As |tan(x+pi)| = |tanx|.

So its period is pi.

And the period of cos2x is (2pi)/2 -------(As period of cosax = (2pi)/|a|).

 

Hence the period of |tanx| + cos2x is pi.

 

Hope this helps.

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Manuj,

 

2. This question involves only drawing the graph of {x}.

As {x} is periodic with period of 1, so any function g({x}) will be periodic with period of 1.

Hence the period of the second question is 1.

 

/ / / / / / / / / / / / / (This represents the graph of {x})

012345678............ (represents the points along the x-axis).

 

Hope it helps.

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

manuj mittal
4 Points
12 years ago

in first question f(x) is even function. therefore period should be equaL to 1/2 L.C.M of {t1,t2}.therefore period must be equal to pi/2.

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Manuj,

 

It is not about f(x) being exen in this case.

You can clearly see that pi/2 is not the period of this function.

 

It will remanin pi only.

As |tanx| and cos2x do not complement each other for pi/2.

(For detailed explanation on this, refer your period-2 Question).

 

With Regards,

Ashwin (IIT Madras).

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