IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

waterdemon

I am giving you all the methods of finding periods of functions :-

1)Sinⁿx , Cosⁿx , secⁿx , cosecⁿx

When n=even number , then period of each one of them will be

When n=Odd number , then period of each one of them will be 2

2)Tanⁿx , Cotⁿx

n=even or Odd . T= (remains the same)

So here The period of [ Cos⁸x + Sin⁸x ] has been asked .

So as n = even so time period of each will be .

After this you are supposed to take

{ LCM of numerator/HCF of Denominator}

In this case there is no denominator so we will just take the LCM of

numerator which is in both.

So LCM is and hence the time period of [ Cos⁸x + Sin⁸x ] is .

In case there is a question like find the period of

f(x) = 3Sin²4x + 4Cos⁴x

Then find the period using the following rules.

1)f(x) has time period as " T ". And then we make it F(x/k) trhen its new

time period will be " TK "

2)f(x) has period " T " and another function is f(Kx) then its new period is

" T/K "

3)f(x) has time period " T " and we make it 2 f(x) then its time period

remains the same.

4)h(x) = LCM (T₁,T₂) when h(x) is not complementary.

5)h(x) = 1/2 LCM (T₁,T₂) when functions of f(x)+g(x) where f(x),g(x) are

complementary .

plZ rate me if you understood.

And if Yes solve the eg: 3Sin²4x + 4Cos⁴x and tell me its time period.

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