Respuesta :
ANSWER
[tex]x=-6.07\degree+n\cdot45\degree[/tex]EXPLANATION
We want to solve the trigonometric equation given:
[tex]8\sin (8x)+9=3[/tex]First, subtract 9 from both sides of the equation:
[tex]\begin{gathered} 8\sin (8x)=3-9 \\ 8\sin (8x)=-6 \end{gathered}[/tex]Then, divide both sides by 8:
[tex]\begin{gathered} \sin (8x)=-\frac{6}{8} \\ \sin (8x)=-\frac{3}{4} \end{gathered}[/tex]Now, apply the trigonometric inverse property i.e. find the sine inverse of both sides of the equation:
[tex]\begin{gathered} 8x=\sin ^{-1}(-\frac{3}{4})+360n \\ 8x=-48.5904+360n \end{gathered}[/tex]where n = 0, 1, 2, 3. . .
Finally, divide both sides by 8:
[tex]\begin{gathered} x=\frac{-48.5904}{8}+\frac{360n}{8} \\ x=-6.07\degree+n\cdot45\degree \end{gathered}[/tex]That is the answer.
