Standard +0.3 This is a straightforward trigonometric equation requiring standard identities (cosec = 1/sin, cot = cos/sin) and manipulation to reach a given quadratic form, followed by routine solving of a quadratic and finding angles. The 'show that' structure provides the key step, making this slightly easier than average but still requiring multiple techniques.
Show that the equation \(\cos ec x + 5 \cot x = 3 \sin x\) may be rearranged as
$$3 \cos^2 x + 5 \cos x - 2 = 0.$$
Hence solve the equation for \(0° \leq x \leq 360°\), giving your answers to 1 decimal place. [7]
Show that the equation $\cos ec x + 5 \cot x = 3 \sin x$ may be rearranged as
$$3 \cos^2 x + 5 \cos x - 2 = 0.$$
Hence solve the equation for $0° \leq x \leq 360°$, giving your answers to 1 decimal place. [7]
\hfill \mbox{\textit{OCR MEI C4 2013 Q2 [7]}}