Express $5$ $\sin 3x - 8$ $\cos 3x$ in the form of $R \sin(3x - \alpha)$ where \(\alpha

Question

Express $5$ $\sin 3x - 8$ $\cos 3x$ in the form of $R \sin(3x - \alpha)$ where $\alpha$ is in radians. Hence, solve $5$ $\sin 3x - 8$ $\cos 3x = -6.5$ for $0 \le x \le \frac{4}{3}\pi$.

Accepted Answer

(i) $\sqrt{89}\sin(3x-1.01)$ (ii) $x=0.0840,\ 1.64,\ 2.18,\ 3.73\text{ rad}$ (3 s.f.)

Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

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