1. ## trig identity equation

"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?

2. Due to $\sin(4x)$ being $\sin(x)$ but "squashed" 4 times as much you will get more solutions.

No identity here though, take the arcsin: $4x = \arcsin(0.48)$

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: