You can revise your knowledge of double angle formulae as part of Expressions and Functions.
Solve the equation \(5\sin 2x^\circ + 7\cos x^\circ = 0\), for \(0^\circ \le x^\circ \le 360^\circ\).
\(5\sin 2x^\circ + 7\cos x^\circ = 0\)
Replace \(\sin 2x^\circ\) with \(2\sin x^\circ \cos x^\circ\)
\(5(2\sin x^\circ \cos x^\circ ) + 7\cos x^\circ = 0\)
Multiply out the brackets:
\(10\sin x^\circ \cos x^\circ + 7\cos x^\circ = 0\)
Take out \(\cos x^\circ\) as the common factor.
\(\cos x^\circ (10\sin x^\circ + 7) = 0\)
Two possible solutions are:
\(\cos x^\circ = 0\)
\(10\sin x^\circ + 7 = 0\)
Solve each equation in turn:
\(x^\circ = 90^\circ\) or \(270^\circ\)
And:
\(10\sin x^\circ = - 7\)
\(\sin x^\circ = - \frac{7}{{10}}\)
\(x^\circ = 224.4^\circ\) or \(315.6^\circ\)
Which gives solutions of \(90^\circ ,\,224.4^\circ ,\,270^\circ ,\,315.6^\circ\)