1. I'm not sure how you're expected to "read off" where they intersect based on an imprecise hand-drawn graph, but we can still find these intersections exactly.
[tex]2\sin(x) = 3 \cos(x)[/tex]
[tex]\dfrac{\sin(x)}{\cos(x)} = \dfrac32[/tex]
[tex]\tan(x) = \dfrac32[/tex]
[tex]x = \tan^{-1}\left(\dfrac32\right) + 180^\circ n[/tex]
where [tex]n[/tex] is an integer.
In the interval [0°, 360°], we have solutions at
[tex]x \approx 56.31^\circ \text{ or } x \approx 236.31^\circ[/tex]
From the sketch of the plot, we do see that the intersections are roughly where we expect them to be. (The first is somewhere between 45° and 90°, while the second is somewhere between 225° and 270°.)
2. According to the plot and the solutions from (1), we have
[tex]3 \cos(x) > 2 \sin(x)[/tex]
whenever [tex]0^\circ < x < 56.31^\circ[/tex] or [tex]236.31^\circ < x < 360^\circ[/tex].
3. Rewrite the inequality as
[tex]2 \sin(x) - 3 \cos(x) \le 0 \implies 3 \cos(x) \ge 2 \sin(x)[/tex]
The answer to (1) tells us where the equality [tex]3\cos(x) = 2\sin(x)[/tex] holds.
The answer to (2) tells us where the strict inequality [tex]3\cos(x)>2\sin(x)[/tex] holds.
Putting these solutions together, we have [tex]2\sin(x) - 3\cos(x) \le 0[/tex] whenever [tex]0^\circ < x \le 56.31^\circ[/tex] or [tex]236.61^\circ \le x < 360^\circ[/tex].
