Question

Give the exact form and decimal form of the equation

8=9sin(6x)

simplify the equation into the form sin(ax)=b and use the inverse sin to solve for x

Answer 1

Exact form:
`sin((6x)) = (8)/(9)`

Decimal form:
`sin((6x)) = 0.8889`

The solution for x is: The solution for x is of 10.455º

Explanation:

We are given the following equation:

`8 = 9sin((6x))`

Placing into the desired format, the exact format is:

`sin((6x)) = (8)/(9)`

In the decimal part, we divide 8 by 9. So

`sin((6x)) = 0.8889`

Solving for x:

We apply the inverse sine. So

`\sin^(-1){sin((6x))} = \sin^(-1){0.8889}`

`6x = 62.73`

`x = (62.73)/(6)`

`x = 10.455`

The solution for x is of 10.455º