# Maths - Superposition of Sine and Cos

> Source: https://ollybritton.com/notes/a-level/maths/topics/superposition-sine-and-cos/ · Updated: 2021-12-05 · Tags: school, maths, year-2

## Flashcards
### 2021-12-05
##### In what form can you express $a\sin x \pm b\cos x$??
$$
R\sin(x \pm \alpha)
$$

##### In what form can you express $a\cos x \pm b\sin x$??
$$
R\cos(x \mp \alpha)
$$

##### You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $R$??
$$
R = \sqrt{a^2 + b^2}
$$

##### You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $\alpha$??
$$
\tan \alpha = \frac{b}{a}
$$

##### You want to express $$a\cos x \pm b\sin x$$ as $$R\cos(x \mp \alpha)$$ How can you calculate $R$??
$$
R = \sqrt{a^2 + b^2}
$$

##### You want to express $$a\cos x \pm b\sin x$$ as $$R\cos(x \mp \alpha)$$ How can you calculate $\alpha$??
$$
\tan \alpha = \frac{b}{a}
$$

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