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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: PERIOD
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v_gurucharan (283)

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PERIOD OF:
 
| SIN(COS X)| +COS(SIN X)

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arpan1 (665)

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ans is /2






rate me

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RyuAmakusa (461)

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PI
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RyuAmakusa (461)

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@arpan1 if period is pi/2 then

| SIN(COS X)| +COS(SIN X) = | SIN(SIN X)| +COS(COS X)

IS THE PERIOD PI/2 OR PI
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arpan1 (665)

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pie/ 2

why r u comparing 2 periods


btw, i think u need to learn certain exceptional cases too

nudge me for the same

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v_gurucharan (283)

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PLS , PROVE HOW IS IT PI ????????

@ RyuAmakusa U R CORRECT!!!!







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v_gurucharan (283)

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IS

cos x + sin ax periodic ????/

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arpan1 (665)

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how can it b pie

i mean both are interchangable functions , arent they ???????

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RyuAmakusa (461)

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COS(SIN X) will repeate the value when SIN X repeates the value

SINCE COS(-SIN X)= COS(SIN X) the value is repeated after pi similarly there is a modulus for the first fn. (you first find the period then check for half of it keep on checking till the half is not a period)
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sboosy (3009)

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\cos(x)+\sin(ax) \\ \\ \mbox{Consider individually} \\ \\ \mbox{Period of} \ \cos(x) = 2\pi \\ \\ \mbox{Period of} \ \sin(ax) = \frac{2\pi}{a} \\ \\ \mbox{Resultant period is LCM of numerators by HCF of denominators} \\ \\ \Rightarrow 2\pi
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arpan1 (665)

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ryu i coulnot  follow that half thing, pls mention it once again

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RyuAmakusa (461)

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i am sorry i was late.

@ arpan1 just check it na f(x)= f(pi+x).

@v_gurucharan did you get it ask if not understood
i think cos x + sin ax is periodic if a
is not equal to t.pi t is any integer
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budokai_tenkaichi (62)

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let it be periodic with period p
|sin(cosx)|+cos(sinx)=|sin(cos(x+p))|+cos(sin(x+p))
on solving................................................................................................
p=n(pie),       n=1,2,3,........
smallest value =period of function =  pie


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budokai_tenkaichi (62)

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also
sinx +cosax
is periodic ,whatever the hell be the value of "a"

Vegeta: While I was with you guys, I became more human. I didn't like that. I even have a family and started to like living on earth.
Vegeta: Don't remind me. I'm mad enough to hurt somebody and pounding you just might be the therapy I need.
Vegeta: You can take control of my mind and my body, but there is one thing a Saiyan always keep... his PRIDE!
[Piccolo and Vegeta sit back to back on a tiny island]
Piccolo: Is it over?
Vegeta: Not until the fish jumps.
[a fish jumps out of the water]
Vegeta: It's over.
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RyuAmakusa (461)

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@arpan1 see first you find the period normaly i mean sinx repeats after 2pi and cos x too. so the period ifs 2pi but now check for 2pi/2 ie pi. check if (x)= f(pi+x). if yes(in this case yes) check for pi/2 it wont satisfy as mentioned previously so pi is the ans.
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