Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

Blazing goIITian

Joined:	22 Jan 2007
Post:	2039

21 Feb 2007 21:29:12 IST

0 People liked this

608

period?

None

Period of   f(x) = |sinx| - |cosx|
                       -----------------------
                        | sinx + cosx |
[ ans :- pie ]

I tried it...

For N^r , period = 1/2 [ LCM(pie, pie)] = pie/2 .....(as numerator is even function)

For D^r, period = LCM(2pie, 2pie ) = 2pie......(as denominator is not even function)

For f(x) , period= LCM(pie/2 , 2pie ) = 2pie......(as f(x) is not even function)
So P=2pie?

Share this article on:

Comments (6)

Manasi

Forum Expert

Joined: 1 Dec 2006

Posts: 2108

21 Feb 2007 22:24:57 IST

Like 0 people liked this

hiiiiiiiii neeraj,

see if we put pi+x in the place of x, we have the same function again.... since sin(pi+x) = -sin x and also cos(pi+x) = -cos x..... so defintely pi will be the period of the funstion....

sometyms even simple analysing the function gives u the value.... for e.g |sinx| + |cos x|...... u might say that both the functions in seperated form has pi as period, but if we put pi/2+x in place of x, we'll again get the same function.....

AAKRITI

Scorching goIITian

Joined: 31 Dec 2006

Posts: 291

21 Feb 2007 23:12:17 IST

Like 0 people liked this

period of |sinx| - |cosx| is pi

and not pi/2

period of |sinx| + |cosx| is pi/2

Neeraj Agarwal

Blazing goIITian

Joined: 22 Jan 2007

Posts: 2039

22 Feb 2007 13:03:18 IST

Like 0 people liked this

AAKRITI

Scorching goIITian

Joined: 31 Dec 2006

Posts: 291

22 Feb 2007 14:11:43 IST

Like 0 people liked this

santa claus

lcm+even/odd method doesn,t always give the right answer

there are many many many exceptions to it.

you can yourself see

in |sinx| - |cosx|,

check for pi/2, function becomes |cosx| - |sinx|

which is not the same , so how can it be periodic with pi/2

Prashant Balasubramanian

New kid on the Block

Joined: 22 Feb 2007

Posts: 2

22 Feb 2007 16:25:49 IST

Like 0 people liked this

the period of the num mod(sinx) as u know is pie, similarly for mod(cosx) is pie... so the period of the num is pie.... as per some aarkita i suppose so ...

the period of the deno is simple mod(sinx + cosx) can be written as mod( sqrt (2) * sin(x+pie/4)) so the perios is just similar to mod(sinx) with a shifted origin so its perios is also pie.

so the perios of the entire function is pie....

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

23 Feb 2007 01:19:08 IST

Like 1 people liked this

Periods of and |sinx| and |cosx| are same i.e.

Hence period of |sinx| - |cosx| is also

.

Period of |sinx + cosx| is

/2.

Hence period of |sinx| - |cosx|
----------------------- is

.
| sinx + cosx |

Lets take example of |sinx|
Its period is

and is an even function.
Then according to u its period should become

which is wrong.

Best Wishes

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team