Range of a function f(x)=cos(k sin x)is [-1,1] then the least positive integral value of k will be?

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Answer 1 · 2018-05-30T15:20:07

#k >= 4#

The range of #ksinx# is #[-k,k]#.

As for #x=0#,

#cos(ksin(x))|_(x=0) = 1#

The range includes #y=1# for any value of #k#.
On the other hand:

#cos(ksinx) = -1 <=> ksinx = pi+2npi#

For #n=0#:

#ksinx = pi#

and as

#ksinx <= k#

Then #k# must be greater that #pi#, which means #k >=4#.