Determine sinus and cosinus : $2\sin x + 3\cos x = 3$

HINT

You have two equations $$ 2\sin(x) + 3\cos(x) = 3\\\sin(x)^2+\cos(x)^2 = 1.$$

Maybe for clarity, replace $\sin$ with $y$ and $\cos$ with $x$ so you have $$ 2y+3x = 3 \\x ^2 + y^2=1.$$

One of these things is a line and one is a circle... find where they intersect. (Further hint: one of these is trivial and one less so.)

This will give the possible values for $\sin(x)$ and $\cos(x)$ which is what you asked for, but if you want the possible values of $x$ there will be an infinite number corresponding to each of the above solutions due to periodicity.