1.8 E: Trigonometry

In a stability analysis for a rotating pendulum, the equilibrium angle $α\alpha$ in the interval $\alpha \le \pi$ satisfies the equation

2\text{cosec}^2 \alpha - 5\cot \alpha = 5

Determine all possible values for $α\alpha$ , giving your answers to 3 significant figures.

[4]

ii.

Prove the following trigonometric identity for all valid values of $θ\theta$ :

\frac{\sin 8\theta}{\sin 3\theta} - \frac{\cos 8\theta}{\cos 3\theta} \equiv \frac{\sin 5\theta}{\sin 3\theta \cos 3\theta}

[3]

In a stability analysis for a rotating pendulum, the equilibrium angle $α\alpha$ in the interval $\alpha \le \pi$ satisfies the equation

2\text{cosec}^2 \alpha - 5\cot \alpha = 5

Determine all possible values for $α\alpha$ , giving your answers to 3 significant figures.

Prove the following trigonometric identity for all valid values of $θ\theta$ :

\frac{\sin 8\theta}{\sin 3\theta} - \frac{\cos 8\theta}{\cos 3\theta} \equiv \frac{\sin 5\theta}{\sin 3\theta \cos 3\theta}

[3]

1.8 E: Trigonometry Questions