If 2sin⁡x−1≤0 and x∈[0,2π]. then the solution set for x, is

If $2 \sin x - 1 \leq 0$ and $x \in [0, 2 π] .$ then the solution set for $x$ , is

A
$[π / 6, 5 π / 6]$
B
$[0, π / 6] \cup [5 π / 6, π]$
C
$[0, π / 6] \cup [5 π / 6, 2 π]$
D
none of these.

Solution:

It is from the graph of $y = \sin x$ that

$\sin x \leq \frac{1}{2}$ for all $x \in [0, π / 6] \cup [5 π / 6, 2 π]$

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