The forms R cos(theta ± a) and R sin(theta ± a)Edexcel International A Level Maths: Mind map

Exam questions on The forms R cos(theta ± a) and R sin(theta ± a)

1. The expression $3\sin\theta+4\cos\theta$ is written in the form $R\sin(\theta+\alpha)$, where $R>0$ and $0<\alpha<90^{\circ}$.
   Hence state the maximum value of $3\sin\theta+4\cos\theta$ and the smallest positive value of $\theta$ at which it occurs, to 1 decimal place.2 marks
2. Let $\mathrm{f}(\theta)=\cos\theta-\sqrt3\sin\theta$, with $\theta$ in radians. It is written in the form $R\cos(\theta+\alpha)$, where $R>0$ and $0<\alpha<\frac{\pi}{2}$.
   Hence find the minimum value of $\mathrm{f}(\theta)$ and the smallest positive value of $\theta$ at which it occurs.2 marks
3. Angles are measured in degrees and a calculator may be used.
   Express $5\cos\theta-12\sin\theta$ in the form $R\cos(\theta+\alpha)$, where $R>0$ and $0<\alpha<90^{\circ}$. Give $\alpha$ to 1 decimal place.3 marks