Final answer:
The question involves solving a trigonometric equation within a given interval. The solution requires using the arcsine function and considering the symmetric properties of the sine function to find two angles that satisfy the equation within the specified interval.
Step-by-step explanation:
The student is asking for the solution to the trigonometric equation 4 sin(x) - 3 = 0 on the interval (10,28), which likely means an interval of angles measured in degrees. To find values of x that satisfy the equation, one would first isolate sin(x) by adding 3 to both sides of the equation and then dividing by 4, resulting in sin(x) = 3/4. We need to find angles for which the sine is 3/4, remembering to consider the principal range for sine, which is between -1 and 1, and knowing that sine is positive in the first and second quadrants.
Using a calculator to find the arcsine (inverse sine), we get a principal value, and then we need to find the second value using the fact that sine is symmetric about 180 degrees. In this context, it's important to keep in mind the given interval (10,28) to find the specific values within this range. Upon finding two such values, we conclude if they are within the specified interval and ensure the answers are reasonable.