Moderate -0.3 This is a standard C2 trigonometric equation requiring the identity cos²x + sin²x = 1 to convert to a quadratic in sin x, then solving using the quadratic formula and finding angles in the given range. It's a textbook exercise with clear steps and no novel insight required, making it slightly easier than average.
3. (i) Show that the equation
$$3 \cos ^ { 2 } x ^ { \circ } + \sin ^ { 2 } x ^ { \circ } + 5 \sin x ^ { \circ } = 0$$
can be written as a quadratic equation in \(\sin \chi ^ { \circ }\).
(ii) Hence solve, for \(0 \leq x < 360\), the equation
$$3 \cos ^ { 2 } x ^ { \circ } + \sin ^ { 2 } x ^ { \circ } + 5 \sin x ^ { \circ } = 0$$