The formulation is not accurate.
The accurate formulation is as follows:


    sin(7x)=0.43. Find the smallest solution, the largest solution and the number of solutions in the interval [,).


OK. Sine has 7 full periods in this interval, and in each period the equation has exactly two solutions,
so the total number of solutions is 2*7 = 14.

To find the smallest, write  7x = arcsin(0.43) = 0.4444 (aproximately). (Here I used my calculator. You can use yours)

Hence, x =  = 0.0635 (approx.). It is the smallest solution.

The next solution after that is  7x = ,

and the largest is   = ,  or

 = .

You can calculate it on your own using this formula.