Solve-for-x-in-0-2pi-sin-4x-pi-6-1-2-

Question Number 94877 by mathocean1 last updated on 21/May/20

Solve for x in [0; 2 π] :

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

Commented by mathocean1 last updated on 21/May/20

Please sir, is there only 2 solutions

\in [0; 2 π] ?

Commented by mathocean1 last updated on 21/May/20

Thank you sir .

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

4 x - \frac{π}{6} = 2 k π + \frac{π}{6} \Rightarrow x = \frac{k π}{2} + \frac{π}{12}

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

w i t h i n [0, 2 π] :

x = \frac{π}{12}, \frac{π}{4}

x = \frac{7 π}{12}, \frac{3 π}{4}

x = \frac{13 π}{12}, \frac{5 π}{4}

x = \frac{19 π}{12}, \frac{7 π}{4}

Commented by ElOuafi last updated on 22/May/20

t h i s i s t h e c o r r e c t a n s w e r s i r (8 s o l u t i o n s)!

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