Express $3$ $\sin x - 2$ $\cos x$ in the form of $R \sin(x - \alpha)$ where $\alpha$

Question

Express $3$ $\sin x - 2$ $\cos x$ in the form of $R \sin(x - \alpha)$ where $\alpha$ is in radians. Hence, solve $3$ $\sin x - 2$ $\cos x = -2.5$ for $0 \le x \le 2\pi$.

Accepted Answer

(i) $\sqrt{13}\sin(x-0.588)$ (ii) $x=4.50\text{ rad}$ or $x=6.11\text{ rad}$ (3 s.f.)

Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

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