91Ó°ÊÓ

Given that \(\alpha\) is a very small angle measured in radians: (a) \(\sin (2 \pi+\alpha)=\sin \alpha\) (b) \(\sin \alpha \simeq \alpha\) (c) \(\sin (2 \pi+\alpha) \simeq 2 \pi+\alpha\) (d) \(\cos \alpha \simeq \alpha\) (e) \(\tan \alpha \simeq \alpha\).

(a) Express \(7 \sin x-24 \cos x\) in the form \(R \sin (x-\alpha)\), where \(R\) is positive and \(\alpha\) is an acute angle. Hence or otherwise solve the equation $$ 7 \sin x-24 \cos x=15, \quad \text { for } 0^{\circ}