Answer:
Exact form: [tex]\sin{(6x)} = \frac{8}{9}[/tex]
Decimal form: [tex]\sin{(6x)} = 0.8889[/tex]
The solution for x is: The solution for x is of 10.455º
Step-by-step explanation:
We are given the following equation:
[tex]8 = 9\sin{(6x)}[/tex]
Placing into the desired format, the exact format is:
[tex]\sin{(6x)} = \frac{8}{9}[/tex]
In the decimal part, we divide 8 by 9. So
[tex]\sin{(6x)} = 0.8889[/tex]
Solving for x:
We apply the inverse sine. So
[tex]\sin^{-1}{\sin{(6x)}} = \sin^{-1}{0.8889}[/tex]
[tex]6x = 62.73[/tex]
[tex]x = \frac{62.73}{6}[/tex]
[tex]x = 10.455[/tex]
The solution for x is of 10.455º
