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harshit agarwal Grade: 12
        

For what integral value of n, is 3π the period of the function


cos(nx) sin(5x/n)

7 years ago

Answers : (1)

Vanya Saxena
18 Points
										

For a function to be periodic f(x+T) = f(x)


i.e.     cos[n(x+T)]sin[5(x+T)/n]=cos(nx)sin(5x/n)


but period of a function is a positive real no. independent of x.


=>cos(nT)sin(5T/n)=0


CASE1


If cos(nT)=0    => nT=[(2K+1)PI/2]     =>3PI(n) =[(2K+1)PI/2]      =>(2K+1)=6n


=>3n-k=1/2      which is not possible as n and k both are integral values


CASE 2


sin(5T/n)=0            =>(5T/n) =(k)pi        =>15/k=n


Now k is an integral value and thus n can attain 8 integral values   ±1 ,±3  ,±5  ,±15

7 years ago
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