First slide

Functions (XII)

Question

$If [5 \sin x] + [\cos x] + 6 = 0, then range of f (x) = \sqrt{3} \cos x + \sin x corresponding to solution set of$
$the given equation is : (where [.] denotes greatest integer function)$

Moderate

A

$[- 2, - 1)$
B

$(- \frac{3 \sqrt{3} + 2}{5}, - 1)$
C

$[- 2, - \sqrt{3})$
D

$(- \frac{3 \sqrt{3} + 4}{5}, - 1)$

Solution

$\begin{array}{l} [5 \sin x] + [\cos x] = - 6 \\ \Rightarrow \begin{aligned} \Rightarrow - 1 \leq \cos x < 0 and \end{aligned} - 5 \leq 5 \sin x < - 4 \\ - 1 \leq \sin x < - \frac{4}{5} \end{array}$

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