Question

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

Answer 1

`k >= 4`

Explanation:

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`.