Compound & Double Angle Formulae (Edexcel A-Level Mathematics): Flashcards

Use $R \cos(\theta \pm \alpha)$ with $R = \sqrt{a^2 + b^2}$.

$R = \sqrt{a^2 + b^2}$, where $a$ and $b$ are coefficients.

$\alpha = \tan^{-1}(b/a)$, relating to $a$ and $b$ coefficients.

Start with $R \cos(\theta - \alpha)$ expansion.

Use $R \sin(\theta \pm \alpha)$ with $R = \sqrt{a^2 + b^2}$.

$R = \sqrt{3^2 + 4^2} = \sqrt{25} = 5$.

$R = 5$, $\alpha = \tan^{-1}(4/3)$, combine to get desired form.

$\theta = \cos^{-1}(2/5) + \alpha$ or $360° - \cos^{-1}(2/5) + \alpha$.

Simplifies analysis of oscillatory motion and waves.

Analyzes AC circuits with sinusoidal voltages and currents.