"For the equation
sin(4 x) = 0.48
find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π."
what identity do I use for this?
Due to $\displaystyle \sin(4x)$ being $\displaystyle \sin(x)$ but "squashed" 4 times as much you will get more solutions.
No identity here though, take the arcsin: $\displaystyle 4x = \arcsin(0.48)$
In case a picture helps - you can ignore the orange line, that's only there to show the difference between sin(4x) and sin(x)
Spoiler: