a) Express $5{\text{ }}\cos \theta - 3{\text{ }}\sin \theta $ in the form $R\cos \left( {\theta + \alpha } \right)$, where $R \gt 0$ and ${0^ \circ } \lt \alpha \lt {90^ \circ }$, giving the exact value of $R$ and the value of $\alpha $ correct to 2 decimal places.
b) Hence solve the equation
$5\cos \theta - 3\sin \theta = 4$,
giving all solutions in the interval ${0^ \circ } \leqslant \theta \leqslant {360^ \circ }$.
c) Write down the least value of $15\cos \theta - 9\sin \theta $ as $\theta $ varies.
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