Given the equation sin(8x) = 4, we first need to recognize that sine of any angle must lie within the range of -1 to 1 (inclusive). Given that 4 is outside this range, it indicates a misunderstanding in the formulation of the problem. Normally, sine values cannot exceed 1 in absolute terms. However, assuming you meant sin(8x) = sin(A) where A is any arbitrary angle, we can apply the inverse sine function to determine the expression for 8x.
To express 8 in terms of x, we can rearrange the standard sine equation. If we use the sine function defined by the formula:
sin(A) = opposite/hypotenuse
We can manipulate this equation to solve for x:
8x = sin-1(4)
Now, dividing both sides by 8, we get:
x = (1/8) * sin-1(4)
In conclusion, the expression for 8 in terms of x using the correct understanding of sine might be presented as:
8 = 8 * (asin(4))