If [$$2$$ $$sin$$ x] $$+$$ [$$cos$$ x] $$=$$ –$$3$$, then the range of the function $$f(x)=$$$$sin$$⁡$$x+3cos$$⁡x in [$$0$$,$$2$$π] (where$$ [⋅] denotes the greatest integer $$function) is

Correct option is 3(–2, –1)

Questions

If [2 sin x] + [cos x] = –3, then the range of the function $f (x) = \sin x + \sqrt{3} \cos x in [0, 2 π]$ (where [⋅] denotes the greatest integer function) is

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[–2, –1]

−1,−12

(–2, –1)

None of these

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detailed solution

Correct option is C

We have, [2 sin x] + [cos x] = –3only if [2 sin x] = –2 and [cos x] = –1⇒ –2 ≤ 2 sin x < –1 and –1 ≤ cos x < 0⇒−1≤sin⁡x<−12 and −1≤cos⁡x<0⇒7π6

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If [2 sin x] + [cos x] = –3, then the range of the function f(x)=sin⁡x+3cos⁡x in [0,2π] (where [⋅] denotes the greatest integer function) is

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If [2 sin x] + [cos x] = –3, then the range of the function $f (x) = \sin x + \sqrt{3} \cos x in [0, 2 π]$ (where [⋅] denotes the greatest integer function) is