Maths - Superposition of Sine and Cos
Pearson Edexcel Mathematics 2022
Flashcards
The R form for sine and cosine combinations
In what form can you express $a\cos x \pm b\sin x$?
\[R\cos(x \mp \alpha)\]
Calculating R and alpha for the sine form
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 $\alpha$?
\[\tan \alpha = \frac{b}{a}\]
Calculating R and alpha for the cosine form
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 $\alpha$?
\[\tan \alpha = \frac{b}{a}\]