Draw the horizontal line \(y = 0.75\). The line \(y = 0.75\) crosses the graph of \(y = \cos{x}\) four times in the interval \(-360^\circ \leq x \leq 360^\circ\) so there are four solutions.

Given any expression of the form \(a\cos x + b\sin x\) it is better to rewrite it into one of the forms \(k\cos (x \pm \alpha )\) or \(k\sin (x \pm \alpha )\) before answering the question.

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