Answer
(a) Amplitude $= 3$, Period $= \frac{\pi}{2}$, refer to graph in picture
(b) Amplitude $= 2$, Period $= 2$, refer to graph in picture
(c) Amplitude $= 1$, Period $= 4 \pi$, refer to graph in picture
Work Step by Step
(a) $y = 3sin (4x)$
Amplitude($A$) $= 3$
Period($T$) $= \frac{1}{f}$
$2 \pi f = 4$
$f = \frac{4}{2 \pi} = \frac{2}{\pi}$
$T = \frac{1}{\frac{2}{\pi}} = \frac{\pi}{2}$
(b) $y = −2 cos πx$
Amplitude($A$) = $2$
$2 \pi f = \pi$
$f = \frac{\pi}{2 \pi} = \frac{1}{2}$
$T = \frac{1}{\frac{1}{2}} = 2$
(c) $y = 2 + cos (\frac{x}{2})$
Amplitude($A$) = $1$
$2 \pi f = \frac{1}{2}$
$f = \frac{\frac{1}{2}}{2 \pi} = \frac{1}{4\pi}$
$T = \frac{1}{\frac{1}{4 \pi}} = 4 \pi$