A continuación, se presentan diferentes funciones periódicas, calcula su periodo y su amplitud segun corresponda. a. \( f(x)=3 \sin (2 x) \) b. \( g(x)=\cos \left(\frac{1}{3} x\right) \) c. \( h(x)=-4 \sin \left(\frac{5}{2} x\right) \) d. \( k(x)=2 \cos (4 x)+1 \) e. \( m(x)=5 \sin \left(\frac{3}{4} x\right)-2 \) f. \( p(x)=-\frac{3}{2} \cos (6 x) \) g. \( q(x)=\sin \left(\frac{x}{2}\right)+\cos (3 x) \) h. \( r(x)=7 \sin \left(\frac{2}{3} x\right) \) i. \( s(x)=\frac{5}{4} \cos \left(\frac{2}{5} x\right) \) i. \( t(x)=4 \sin (8 x)+3 \)

(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 \( \triangle \mathrm{GHI}, g=9.6 \) 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 \( \triangle \mathrm{PQR}, p=4.7 \) 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 \( \triangle X Y Z, x=410 \) inches, \( y=450 \) inches and \( z=210 \) inches. Find the measure of \( \angle X \) to the nearest degree.

In \( \triangle \mathrm{EFG}, f=400 \) inches, \( m \angle \mathrm{~F}=94^{\circ} \) and \( m \angle \mathrm{G}=33^{\circ} \). Find the length of \( g \), to the nearest 10th of an inch.