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Chapter 9: Problem 4
An arc of a circle, radius \(5 \mathrm{~cm}\), subtends an angle of \(\frac{3 \pi}{4}\) radians at the centre. Calculate the length of the arc.
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Show $$ \frac{\sin 3 A}{\sin 2 A}=2 \cos A-\frac{1}{2 \cos A} $$
A current, \(i(t)\), varies with time, \(t\), and is given by $$ i(t)=30 \cos (t-0.4) \quad t \geq 0 $$ (a) Find the time when the current is first zero. (b) Find the time when the current reaches its first peak.
Simplify \(\sin \theta \cos \theta \tan \theta+\cos ^{2} \theta\)
Verify the identity $$ 2 \sin A \sin B=\cos (A-B)-\cos (A+B) $$ with \(A=50^{\circ}\) and \(B=15^{\circ}\).
Show \(\sin \left(\theta+\frac{\pi}{2}\right)=\cos \theta\)
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