Solve-in-0-2pi-2sin-4x-pi-6-1-Please-sirs-

Question Number 94910 by mathocean1 last updated on 21/May/20

Solve in [0; 2 π]

2 \sin (4 x - \frac{π}{6}) ⩾ 1

Please sirs \dots

Answered by mr W last updated on 21/May/20

\sin (4 x - \frac{π}{6}) ⩾ \frac{1}{2}

2 k π + \frac{π}{6} ⩽ 4 x - \frac{π}{6} ⩽ 2 k π + π - \frac{π}{6}

\Rightarrow \frac{k π}{2} + \frac{π}{12} ⩽ x ⩽ \frac{k π}{2} + \frac{π}{4} w i t h k \in Z

w i t h i n [0, 2 π] :

\frac{π}{12} ⩽ x ⩽ \frac{π}{4}

\frac{7 π}{12} ⩽ x ⩽ \frac{3 π}{4}

\frac{13 π}{12} ⩽ x ⩽ \frac{5 π}{4}

\frac{9 π}{12} ⩽ x ⩽ \frac{7 π}{4}

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