What is the maxima and minima value of sinx+sin2x+sin4x+sin5x?

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Answer 1 · 2018-05-08T06:49:53

minimum value of # f(x)=-4#
maximum value of #f(x)=+4#

Let,

#f(x)=sinx+sin2x+sin4x+sin5x#

We know that, range of sine is : #[-1,1]#

#i.e. -1 <= sintheta <= 1#

Substituting, #theta=x,2x,4x,5x# respectively,we get

#-1 <=sinx <= 1....to(1)#
#-1 <=sin2x <= 1...to(2)#
#-1 <=sin4x <= 1...to(3)#
#ul(-1 <=sin5x <= 1...to(4)#
#-4<=f(x) <=4...to[(1)+(2)+(3)+(4)]#

Hence,

range of #f(x) , is :[-4,4]#