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Period of f(x)=sin 4 x + cos 4 x is ??? How???

Period of f(x)=sin4x + cos4x is ??? How???

Grade:12th Pass

2 Answers

Swapnil Saxena
102 Points
10 years ago

Differentiate the function with respect to x.

d/dx of sin^4(x)+cox^4(x)=4sin^3(x)cos(x)-4cos^(x)sin(x)

Putting it equal to 0.

=4sin^3(x)cos(x)-4cos^(x)sin(x)=0

=4sin(x)cos(x)(sin^2(x)-cos^2(x))=0

sin(x)cos(x)=0 or sin^2(x)-cos^2(x)=0

If sin(x)=0,x=0 or cos(x)=0,x=(pie/2) (MAXIMA OF THE FUNCTION)

If sin^2(x)-cos^2(x)=0 then sin^2(x)=cos^2(x) or x=(pie)/4 or x=3(pie)/4 (MINIMA OF THE FUNCTION)

Since the function  has the same value after an interval of pie/2, So the period must be (pie)/2.

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Aditi,

 

As powers of sin and cos are even, and we have the sum of both sin and cos, they both can interchange and add.

ie A+B is same as B+A.

 

So period of the above function will be pi/2.

 

Best Regards,

Ashwin (IIT Madras).

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