6) Solve the trigonometric equations over the interval \( 0 \leq x \leq 2 \pi \) a) \( 2 \sin 2 x-\sin x=0 \) b) \( \cos 2 x+\sin ^{2} x-4 \cos x+3=0 \) c) \( 2 \csc x^{2}-8=0 \) ( \( 2=0 \)

In \( \triangle \mathrm{PQR}, p=4.7 \) inches, \( m \angle \mathrm{P}=76^{\circ} \) and \( m \angle \mathrm{Q}=57^{\circ} \). Find the length of \( q \), to the nearest 10th of an inch.

In \( \triangle \mathrm{GHI}, g=9.6 \) inches, \( m \angle \mathrm{I}=80^{\circ} \) and \( m \angle \mathrm{G}=15^{\circ} \). Find the length of \( h \), to the nearest 10th of an inch.

In \( \triangle \mathrm{FGH}, f=7.4 \) inches, \( g=1 \) inches and \( h=7 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest degree.

(c) \( \sin (\pi+x)+\cos \left(\frac{\pi}{2}-x\right)+\tan \left(\frac{\pi}{2}+x\right)+\tan \left(\frac{3 \pi}{2}-x\right) \)

In \( \triangle \mathrm{IJK}, k=1.9 \) inches, \( m \angle \mathrm{~J}=59^{\circ} \) and \( m \angle \mathrm{~K}=18^{\circ} \). Find the length of \( j \), to the nearest 10 th of an inch.