Expressed in the form $R\sin(x-\beta)$, the expression $3\sin x-2\cos x$ has:

1. Expand the target form: $R\sin(x-\beta)=R\sin x\cos\beta-R\cos x\sin\beta$. 2. Match coefficients: $R\cos\beta=3$ and $R\sin\beta=2$. 3. Squaring and adding: $R^2=3^2+2^2=13$, so $R=\sqrt{13}$. 4. Dividing: $\tan\beta=\dfrac23$, so $\beta=33.69^{\circ}$. 5. $R=5$ adds the coefficients instead of their squares; $56.31^{\circ}$ inverts the tangent ratio. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 5: Trigonometry_