Answer
(a) Amplitude($A$) $= 4$
Period($T$) $= \pi$
(b) Amplitude($A$) $= \frac{1}{2}$
Period($T$) $= \frac{2 \pi}{3}$
(c) Amplitude($A$) $= 4$
Period($T$) $= 6 \pi$
Work Step by Step
(a) $y = −1 − 4 sin 2x$
Amplitude($A$) $= 4$
Period($T$) $= \frac{1}{f}$
$2 \pi f = 2$
$f = \frac{2}{2 \pi} = \frac{1}{\pi}$
$T = \frac{1}{\frac{1}{\pi}} = \pi$
(b) $y = \frac{1}{2} cos(3x − π)$
Amplitude($A$) $= \frac{1}{2}$
$2 \pi f = 3$
$f = \frac{3}{2 \pi} = \frac{3}{2 \pi}$
$T = \frac{1}{\frac{3}{2\pi}} = \frac{2 \pi}{3}$
(c) $y = −4 sin ( \frac{x}{3} + 2π)$
Amplitude($A$) $= 4$
$2 \pi f = \frac{1}{3}$
$f = \frac{\frac{1}{3}}{2 \pi} = \frac{1}{6 \pi}$
$T = \frac{1}{\frac{1}{6 \pi}} = 6 \pi$
