Make x the subject of the equation.

[rollcast]

1. The problem statement, all variables and given/known data

Make x the subject of the formula

sin(5x-24)=0.6

2. Relevant equations

sin(5x-24)=0.6

3. The attempt at a solution

sin(5x-24)=0.6
5x-24=sin^-1(0.6)
x=(sin^-1(0.6)+24)/5

[Mello]

You had it right I believe, what exactly is your question?

sin(5x-24) = 0.6

5x - 24 = arcsin(0.6)

5x = 24 + arcsin(0.6)

x = [24 + arcsin(0.6)] / 5

X = ~12.174

[SteamKing]

Or, if (5x-24) is measured in radians, x is about 4.93.

[eumyang]

There should be an infinite number of solutions, shouldn't there? Remember that the range of the arcsin function is only [-π/2, π/2].