Standard +0.8 This is a two-part harmonic form question requiring standard R-cos(x-α) conversion followed by a non-trivial trigonometric equation. Part (i) is routine C3 content, but part (ii) requires recognizing that 6cos²x + sin2x can be rewritten using the double angle formula and cos²x = (1+cos2x)/2, then connecting it to part (i). The multi-step algebraic manipulation and the need to find all solutions in the given range elevate this above average difficulty, though it remains within standard C3 scope.
6. (i) Express \(3 \cos x ^ { \circ } + \sin x ^ { \circ }\) in the form \(R \cos ( x - \alpha ) ^ { \circ }\) where \(R > 0\) and \(0 < \alpha < 90\).
(ii) Using your answer to part (a), or otherwise, solve the equation
$$6 \cos ^ { 2 } x ^ { \circ } + \sin 2 x ^ { \circ } = 0$$
for \(x\) in the interval \(0 \leq x \leq 360\), giving your answers to 1 decimal place where appropriate.
6. (i) Express $3 \cos x ^ { \circ } + \sin x ^ { \circ }$ in the form $R \cos ( x - \alpha ) ^ { \circ }$ where $R > 0$ and $0 < \alpha < 90$.\\
(ii) Using your answer to part (a), or otherwise, solve the equation
$$6 \cos ^ { 2 } x ^ { \circ } + \sin 2 x ^ { \circ } = 0$$
for $x$ in the interval $0 \leq x \leq 360$, giving your answers to 1 decimal place where appropriate.\\
\hfill \mbox{\textit{OCR C3 Q6 [8]}}