The R-formula (a cos + b sin)AQA A-Level Maths: Mind map

Exam questions on The R-formula (a cos + b sin)

1. Let $f(\theta)=3\cos\theta+4\sin\theta$, with $\theta$ in degrees. It is written in the form $r\cos(\theta-\alpha)$, where $r>0$ and $0^\circ<\alpha<90^\circ$.
   Write down the maximum value of $f(\theta)$ and the smallest positive value of $\theta$ at which it occurs.2 marks
2. Let $g(\theta)=\sqrt3\sin\theta-\cos\theta$, with $\theta$ in degrees. It is written in the form $R\sin(\theta-\alpha)$, where $R>0$ and $0^\circ<\alpha<90^\circ$.
   Solve $g(\theta)=1$ for $0^\circ\le\theta\le360^\circ$.2 marks
3. Let $h(x)=5\sin x+12\cos x$, where $x$ is in degrees.
   Express $h(x)$ in the form $R\sin(x+\alpha)$, where $R>0$ and $0^\circ<\alpha<90^\circ$.3 marks