IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

waterdemon

Sorry for making it late

Complementary functions mean that have same nature of graphs.

Sinx is an od function whereas Cosx is an evenfunction .

Hope you understood.

Goodnight and Cheers !!!!!!!!!!!!!!!!!!!!!!

waterdemon

Here are some more for all of you.

1) f(x) = ISin2xI + 3ICos2xI

2) f(x) = 3Sin(

x/3) + 4Cos(

x/4)

3) f(x) = e^{Cos (pi)x + x - [x]} + Tan³x

Period of x - [x] = period of {x} = 1

Solve , its for all of them who wish to solve.

Cheers !!!!!!!!!!!!!!!

abhijeet_0201

well i am not sure but
1)pie/2

waterdemon

Oh !!!!

Good job.

See, 1) ISin2xI + 3ICos2xI

so period of ISinxI = and since it is ISin2xI so T = /2

For ICosxI period is and since it is ICos2xI so T = /2

The LCM is and HCF of Denominator is 2

So T₀ = /2

Sinx and Cosx are complemantary

But on drawing the graph ISinxI and ICosxI are same in nature.

That is symmetrical about Y axis.

So T₀=/4

Cheers !!!!!!!!!!!!!!!!

neeraj_agarwal_1990

u find it to be pi...then check if there exists any other value(+ve and non zero) for which u may get the same function.....it is pi/2!

joyfrancis

sin^8(x+pi/2) + cos^8(x+pi/2)
=sin^8x - cos^8x

pi/2 is not the period, its pi only.

neeraj_agarwal_1990

common!!!
it is even power of cos so (-cosx)^8=cosx^8!

abhijeet_0201

neeraj_agarwal_1990
is correct the ans given to my very first prob is pie/2 and not pie

@waterdemon

well in ur method u said that if complemetary func are there then only we divide by2

sin^8x and cos^8x are not complementary(both are even)
so why is the answer pie/2????????

joyfrancis

oh yes neeraj_agarwal_1990 is right. Good work.

karthik2007

Here I go:

1. Period is pi/2 (Complementary functions)
2.is the period 12?
3.Period is Pi?

waterdemon

Hello many arguments wow

It feels good to know that all are taking intereest in the question

For complementary what is cmplementary

Sinx = Cox(90 - x)

Now ISinxI + ICosxI = on drawing the graph we will find that both are symmetric in the same way that is about Y axis

So they are complementary.

But for Sin^8x + Cos^8x the fgraph is not complementary as Sin^8x

remains symmetrical about the origin diagonallyand Cos^8 (x)

is symmetric about Yaxis.

So in Sin^8 (x) + Cos^8 (x) T = pi as n=8 [ even ]

And f(x) is not complementary in graph

So yes the T = pi

Cheers !!!!!!!!!!!!!!!!!!!!!!!!

waterdemon

sorry to every one

that is what is good about this site , everyone is there to correct yo if you are wrong at some point

That's the spirit GOIITIANS .

Actually was solving in the night and may have gotsomewhat lousy so a minor mistake.

Cheers !!!!!!!!!!!!!!!!!!!!

waterdemon

No

I am sure that the answer is "pi"

Check the solution given there there is some mistake.

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